Exercise 39 Page 26

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