Exercise 70 Page 63

Rewrite the given expression so that it is possible to make groups.

10(x-y)^2

Practice makes perfect

We want to factor the given polynomial. 10x^2-20xy+10y^2 Let's start by identifying the greatest common factor (GCF).

Factor Out the GCF

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 10.

10x^2-20xy+10y^2

SplitIntoFactors

Split into factors

10(x^2)- 10(2xy)+ 10(y^2)

FactorOut

Factor out 10

10(x^2-2xy+y^2)

Factor the Trinomial

Let's start by writing the middle term as a difference of two terms. Then we will take the greatest common factor of each pair of the terms so we can factor by grouping.

10(x^2-2xy+y^2)

WriteDiff

Write as a difference

10( x^2 - xy-xy+y^2)

FactorOut

Factor out x

10(x( x-y ) - xy + y^2)

FactorOut

Factor out - y

10(x( x-y ) -y( x-y ))

Notice that (x-y) is a factor of both terms, so we can factor it out.

10(x( x-y ) -y( x-y ))