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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 39 Page 26

Apply the Distributive Property.

x^2-10xy+25y^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.

(x-5y)^2
PowToProdTwoFac

a^2=a* a

(x-5y)(x-5y)
Distr

Distribute (x-5y)

x(x-5y)-5y(x-5y)
Distr

Distribute x

x^2-5xy-5y(x-5y)
Distr

Distribute -5y

x^2-5xy-5xy+25y^2
SubTerm

Subtract term

x^2-10xy+25y^2

Alternative Solution

 Expanding Negative Perfect Square
We can also simplify the expression by expanding the negative perfect square trinomial.

(x-5y)^2
ExpandNegPerfectSquare

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

x^2-2x(5y)+(5y)^2
PowProdII

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

x^2-2x(5y)+5^2y^2
CalcPow

Calculate power

x^2-2x(5y)+25y^2
Multiply

Multiply

x^2-10xy+25y^2
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