Easy Algebra Step-by-Step

122 Easy Algebra Step-by-Step

= 4 xy^63 ⋅ 32 xy^26 − 444 xyxy^34 ⋅ 22 z^2

Step 3. Use the distributive property to factor 4x^6 y^3

from the resulting expression.

= 4 x^6 y^3 (3x^2 − 2 y^4 z^2 )

Step 3. Review the main steps.

12 x^83 y − 88 xy^67 zx^26444 y^3 () 3233 x^2 yz^424

b. 15 x^2 − 3 x

Step 1. Determine the GCF for 15x^2 and 3x.

GCF = 3 x

Step 2. Rewrite each term of the polynomial as

an equivalent product of 3x and a second

factor.

15 3

xx^23

=^33 xx⋅^5 x−^3 ⋅^1

Step 3. Use the distributive property to factor 3x from the resulting

expression.

= 3 x(5x − 1)

Step 4. Review the main steps.

15 xx^23333 x() 515 x

c. x^3 y − xy + y

Step 1. Determine the GCF for x^3 y, xy, and y.

GCF = y

Step 2. Rewrite each term of the polynomial as an equivalent product of y

and a second factor.

xy^3 −+xyxy y

=yy⋅ −y⋅x+⋅y

(^31)
Step 3. Use the distributive property to factor y from the resulting
expression.
= y(x^3 − x + 1)
12 x^8 y^3 −^8 x^6 y^7 z^2 is not in factored
form because it is not a product,
but 4x^6 y^3 (3x^2 − 2 y^4 z^2 ) is in
factored form because it is the
product of 4x^6 y^3 and (3x^2 − 2 y^4 z^2 ).
15 x^2 − 3 x ≠ 3 x ⋅ 5 x − 0; ask
yourself, “What times 3x equals
3 x?” The answer is 1, not 0.
Remember to mentally multiply
the factors to check your work.