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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 39 Page 82

Factor out the greatest common factor of the first pair of terms and the greatest common factor of the second pair of terms.

(2x-3z)(x-y)

Practice makes perfect

To factor by grouping we will take the greatest common factor of the first pair of terms and the greatest common factor of the second pair of terms.

2x^2-3xz - 2xy+3yz

Factor out 2x

2x(x-y) - 3xz + 3yz

Factor out - 3z

2x(x-y)-3z(x-y)

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

2x(x-y)-3z(x-y)

Factor out ( x-y )

( 2x-3z ) ( x-y )

Checking Our Answer

Check your answer ✓

To check our answer, we can apply the Distributive Property and compare the result with the given expression.

(2x-3z)(x-y)

Distribute (x-y)

2x(x-y)-3z(x-y)

Distribute 2x

2x^2-2xy-3z(x-y)

Distribute - 3z

2x^2-2xy-3xz+3yz

After applying the Distributive Property the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85