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Published byJenna Thomson Modified over 2 years ago

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Multiplying Binomials Mentally

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The Distributive Property (x + 5)(2x + 6) (x+5) 2x + (x+5)6 2x(x+5) +6(x+5) 2x² + 10x + 6x x² + 16x +30 NOTE : Since there are THREE terms this is called a TRINOMIAL

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Trinomials Multiplying MOST binomials results in THREE terms You can learn to multiply binomials in your head by using a method called F O I L

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The FOIL Method (x + 4)(x +2) first terms last terms (x + 4) ( x + 2) inner terms outer terms

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(x + 4) ( x + 2) Now write the products x² + 2x + 4 x + 8 first outer inner last terms terms terms terms

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To Multiply any two binomials and write the result as a TRINOMIAL follow these steps multiply the first two terms multiply the two outer terms multiply the two inner terms multiply the last two terms

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Special Cases There are several special cases of multiplying binomials Difference of Squares Perfect Square Trinomials

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Difference of two squares When you multiply the sum of two terms and the difference of two terms you get a BINOMIAL (a + b) (a – b) = a² - b² This binomial is the difference of two squares

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A Closer Look (k – 4) (k + 4) Using FOIL k ² + 4k - 4k - 16 k ² - 16 (6c – 3) ( 6c + 3) Using FOIL 36c² +18c – 18c – 9

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Squaring A Binomial When you square any binomial(that is multiply it by itself) you get a TRINOMIAL (x+9)² means (x+9)(x+9) Using FOIL x² + 9x + 9x + 81 x² + 18x +81 This is called a PERFECT SQUARE TRINOMIAL

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REMEMBER: The square of a binomial is the sum of three things: The square of the first term Twice the product of the terms The square of its last term

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Perfect Square Trinomials (3x – 6 )² = (3x - 6) (3x – 6) 9x² – 36 x + 36 (2m –4)² = (2m - 4)( 2m – 4) 4m² –16m + 16

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An example (6x + 3)² The square of the first term: 36 x² Twice the product of the terms 2( 6x 3) +36 x The square of the last terms (3)(3) +9 36x² + 36x + 9

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Perfect Square Trinomial patterns (a + b)² = a² + 2ab + b² ( a – b)² = a ² - 2ab + b²

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