144 algebra De mystif ieD
PRACTICE
Factor a negative quantity from the expression.
- 28xy^2 − 14x =
- 4x + 16xy =
- −18y^2 + 6xy =
- 25 + 15y =
- −8x^2 y^2 − 4xy^2
- −18x^2 y^2 − 24xy^3 =
- 20xyz^2 − 5yz =
✔SOLUTIONS
- 28xy^2 − 14x = −7x(−4y^2 + 2)
- 4x + 16xy = −4x(−1 − 4y)
- −18y^2 + 6xy = −6y(3y − x)
- 25 + 15y = −5(−5 − 3y)
- −8x^2 y^2 − 4xy^2 = −4xy^2 (2x + 1)
- −18x^2 y^2 − 24xy^3 = −6xy^2 (3x + 4y)
- 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).