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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Multiplying Polynomials

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Exercise 37 Page 26

Apply the Distributive Property.

a^2-4ab+4b^2

Practice makes perfect

We can find the product of this expression using polynomial identities. In this case, we have the square of a binomial. We will first rewrite the square as the product and then apply the Distributive Property.

(a-2b)^2

PowToProdTwoFac

a^2=a* a

(a-2b)(a-2b)

Distribute (a-2b)

a(a-2b)-2b(a-2b)

Distribute a

a^2-2ab-2b(a-2b)

Distribute -2b

a^2-2ab-2ab+4b^2

Subtract term

a^2-4ab+4b^2

Alternative Solution

Expanding Negative Perfect Square

We can also simplify the expression by expanding the negative perfect square trinomial.

(a-2b)^2

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

a^2-2a(2b)+(2b)^2

(a b)^m=a^m b^m

a^2-2a(2b)+2^2b^2

Calculate power

a^2-2a(2b)+4b^2

Multiply

a^2-4ab+4b^2

Subchapter links

Exercises p.25-27