Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 137

PRACTICE

Use the distributive property to rewrite the expression.

1. −2(16 + y) =


2. −50(3 − x) =


3. −12xy(−2x + y) =


4. −7x^2 (−x − 4y) =


5. −6y(−3x − y + 4) =

✔SOLUTIONS

1. −2(16 + y) = −32 − 2y


2. −50(3 − x) = −150 + 50x


3. −12xy(−2x + y) = 24x^2 y − 12xy^2


4. −7x^2 (−x − 4y) = 7x^3 + 28x^2 y


5. −6y(−3x − y + 4) = 18xy + 6y^2 − 24y

Combining Like Terms

Two or more terms are alike if they have the same variables and the exponents

(or roots) on those variables are the same: 3x^2 y and 5x^2 y are like terms but 6xy

and 4xy^2 are not. Constants are terms with no variables. The number in front

of the variable(s) is the coefficient—in the expression 4x^2 y^3 , 4 is the coefficient.

If no number appears in front of the variable, then the coefficient is 1. We add

and subtract like terms by adding or subtracting their coefficients.

EXAMPLES

Combine like terms.

3 x^2 y + 5x^2 y

Both terms are alike because they have the same variables with the

same exponents, so we simply add the coefficients 3 and 5, to obtain,

3 x^2 y + 5x^2 y = (3 + 5)x^2 y = 8x^2 y.

14 xx–= 10 () 14 − 10 xx= (^4)
8 xyz + 9xyz – 6xyz = (8 + 9 – 6)xyz = 11xyz
3 x + x = 3x + 1x = (3 + 1)x = 4x
PRACTICE
Use the distributive property to rewrite the expression.

1. −2(16 +

PRACTICE

Use the distributive property to rewrite the expression.

EXAMPLES

Combine like terms.