144 algebra De mystif ieD

PRACTICE

Factor a negative quantity from the expression.

1. 28xy^2 − 14x =


2. 4x + 16xy =


3. −18y^2 + 6xy =


4. 25 + 15y =


5. −8x^2 y^2 − 4xy^2


6. −18x^2 y^2 − 24xy^3 =


7. 20xyz^2 − 5yz =

✔SOLUTIONS

1. 28xy^2 − 14x = −7x(−4y^2 + 2)


2. 4x + 16xy = −4x(−1 − 4y)


3. −18y^2 + 6xy = −6y(3y − x)


4. 25 + 15y = −5(−5 − 3y)


5. −8x^2 y^2 − 4xy^2 = −4xy^2 (2x + 1)


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


7. 20xyz^2 − 5yz = −5yz(−4xz + 1)

PRACTICE

Factor a negative quantity from the expression.

still struggling

the distributive property and the associative property of multiplication can be

confusing because both involve parentheses and multiplication. the associative

property involves the product of three quantities, (ab)c = a(bc). this property

says that when multiplying three quantities we can multiply the first two then

the third, or multiply the second two then the first. For example, it might

be tempting to write 5(x + 1)(y – 3) = (5x + 5)(5y – 15). but (5x + 5)(5y – 15) =

[5(x + 1)][5(y – 3)] = 25(x + 1)(y – 3). the “5” can be grouped either with “x + 1”

or with “y – 3” but not both. the correct computation is either [5(x + 1)](y – 3) =

(5x + 5)(y – 3) or (x + 1)[5(y – 3)] = (x + 1)(5y – 15).

?

Factors themselves can have more than one term. For instance 3(x + 4) – x(x + 4)

has x + 4 as a factor in each term, so x + 4 can be factored from 3(x + 4) and

from x(x + 4): 3(x + 4) – x(x + 4) = (3 – x)(x + 4).