Topic: Multiplying Polynomials. Multiplying Polynomials REMEMBER: Laws of exponents. REMEMBER: Combine like terms for your final answer (exponents don’t.

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Presentation transcript:

Topic: Multiplying Polynomials

Multiplying Polynomials REMEMBER: Laws of exponents. REMEMBER: Combine like terms for your final answer (exponents don’t change). REMEMBER: Final answer should be in standard form.

Multiplying Polynomials: Distribution Distribute 2x 2 y to each term. Simplify each term. Remember exponent rules. Since these two terms can’t be combined, this is our final answer.

“FOIL” method for multiplying binomials “F”: multiply first terms in each binomial (x & 4x). “O”: multiply the outer terms in the binomial (x & -1). Combine like terms & write final answer in standard form. Multiplying Polynomials: Distribution “I”: multiply the inner terms in the binomial (6 & 4x). “L”: multiply the last terms in the binomial (6 & -1).

“Everybody meets everybody at the polynomial party.” Distribute 5x to each term (5x “meets” everybody). Distribute 3 to each term (3 “meets” everybody). Combine like terms & write final answer in standard form (50x 2 & 6x 2 combine; -30x & 30x combine…& eliminate). Multiplying Polynomials: Distribution JOURNAL ENTRY: Title – Distribution vs. FOIL Explain in your own words how distribution & the “FOIL” method are similar. Do you believe it’s better to think in terms of distribution or “FOIL?” Defend your belief.

Multiplying Polynomials: Algebraic Punnett Square Create a grid based on the number of terms in each polynomial (in this case 3 x 2). Place each term from each polynomial outside the grid. Fill in each box by multiplying the proper terms. Combine like terms & write final answer in standard form.

Special Products Binomial squared Will always multiply to a “perfect-square trinomial”. First term of the answer will be the square of the first term in the binomial. 2 nd term of the answer will be twice the product of the 2 binomial terms. 3 rd term of the answer will be the square of the second term in the binomial. You could also rewrite the problem as (3x + 7)(3x + 7) & use distribution or Algebraic Punnett Square, but if we recognize & remember the shortcut, life is a lot easier!

Special Products Product of conjugates Conjugates are similar to additive inverses, except for binomials. Binomial conjugates would be in the form (x + a) & (x – a). Will always multiply to a “difference of squares”. First term of the answer will be the product of the first terms in each binomial. 2 nd term of the answer will be the product of the second terms in each binomial. Again, you could multiply this out & combine like terms, but you will find that the middle, x term will always cancel out. In other words, these are like “FOIL” without the “OI”.

Homework Quest: Multiplying Polynomials DUE 2/29 (A-day) or 3/1 (B-day)