Multiplying Polynomials. Multiply monomial by polynomial.

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Presentation transcript:

Multiplying Polynomials

Multiply monomial by polynomial

Multiply polynomial by polynomial

Multiply two binomials

Multiply the Sum and the Difference of Two Terms

Squaring a Binomial

1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

18a²b – 2ab 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

4a² – 16 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

4a² – 16 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

n² GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

n² + 36 Prime! 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² = ( )² + 2( )( ) +( )² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² = (5a)² + 2( )( ) +(b)² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² = (5a)² + 2(5a)(b) +(b)² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

25a² + 10ab + b² = (5a)² + 2(5a)(b) +(b)² = (5a + b)² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = = (2a)³ + (5)³ 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = = (2a)³ + (5)³ =(2a + 5)(4a² - 10a + 25) 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = = (2a)³ + (5)³ =(2a + 5)(4a² - 10a + 25) (2a)² (5)² 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = = (2a)³ + (5)³ =(2a + 5)(4a² - 10a + 25) (2a)² (5)² (2a)(5) 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

8a³ = = (2a)³ + (5)³ =(2a + 5)(4a² - 10a + 25) 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x² - 5x +6 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x² - 5x +6 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x² - 5x +6 = (x )(x ) GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x² - 5x +6 = (x )(x ) GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x² - 5x +6 = (x – 2)(x – 3) GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

xy – 6x +7y – 42 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

xy – 6x +7y – 42 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

xy – 6x +7y – 42 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x 6x² - 7x - 5 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

x 6x² - 7x - 5 = BOX! Always factor completely!

x 6x² - 7x - 5 =

x 6x² - 7x - 5 = 6x² - 5

x 6x² - 7x - 5 = 3x 2x 6x² - 5

6x² - 7x - 5 = 3x - 5 2x 1 6x² - 5

x 6x² - 7x - 5 = 3x - 5 2x 1 6x² - 10x 3x - 5

6x² - 7x - 5 = 3x - 5 2x x + 3x = - 7x 6x² - 10x 3x - 5

6x² - 7x - 5 = (2x + 1)(3x - 5) 3x - 5 2x x + 3x = - 7x 6x² - 10x 3x - 5

(3x - 5)² - 6(3x - 5) + 9 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!

(3x - 5)² - 6(3x - 5) + 9 = 1.GCF (if any) 2.a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2ab + b²) a³ + b³ = (a + b)(a²-2ab + b²) 3. a² + 2ab + b² = (a + b)² a² - 2ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4.If 4 or more terms, try to factor by Grouping Always factor completely!