# Find the GCF a^2b^2(a^2+ab+b^2) , a^3b^3(a^3-b^3)

a2b2(a2+ab+b2) , a3b3(a3-b3)
Simplify each term.
Apply the distributive property.
a2b2a2+a2b2(ab)+a2b2b2,a3b3(a3-b3)
Simplify.
Multiply a2 by a2 by adding the exponents.
Move a2.
a2a2b2+a2b2(ab)+a2b2b2,a3b3(a3-b3)
Use the power rule aman=am+n to combine exponents.
a2+2b2+a2b2(ab)+a2b2b2,a3b3(a3-b3)
a4b2+a2b2(ab)+a2b2b2,a3b3(a3-b3)
a4b2+a2b2(ab)+a2b2b2,a3b3(a3-b3)
Multiply a2 by a by adding the exponents.
Move a.
a4b2+a⋅a2b2b+a2b2b2,a3b3(a3-b3)
Multiply a by a2.
Raise a to the power of 1.
a4b2+a⋅a2b2b+a2b2b2,a3b3(a3-b3)
Use the power rule aman=am+n to combine exponents.
a4b2+a1+2b2b+a2b2b2,a3b3(a3-b3)
a4b2+a1+2b2b+a2b2b2,a3b3(a3-b3)
a4b2+a3b2b+a2b2b2,a3b3(a3-b3)
a4b2+a3b2b+a2b2b2,a3b3(a3-b3)
Multiply b2 by b2 by adding the exponents.
Move b2.
a4b2+a3b2b+a2(b2b2),a3b3(a3-b3)
Use the power rule aman=am+n to combine exponents.
a4b2+a3b2b+a2b2+2,a3b3(a3-b3)
a4b2+a3b2b+a2b4,a3b3(a3-b3)
a4b2+a3b2b+a2b4,a3b3(a3-b3)
a4b2+a3b2b+a2b4,a3b3(a3-b3)
Multiply b2 by b by adding the exponents.
Move b.
a4b2+a3(b⋅b2)+a2b4,a3b3(a3-b3)
Multiply b by b2.
Raise b to the power of 1.
a4b2+a3(b⋅b2)+a2b4,a3b3(a3-b3)
Use the power rule aman=am+n to combine exponents.
a4b2+a3b1+2+a2b4,a3b3(a3-b3)
a4b2+a3b1+2+a2b4,a3b3(a3-b3)
a4b2+a3b3+a2b4,a3b3(a3-b3)
a4b2+a3b3+a2b4,a3b3(a3-b3)
Apply the distributive property.
a4b2+a3b3+a2b4,a3b3a3+a3b3(-b3)
Multiply a3 by a3 by adding the exponents.
Move a3.
a4b2+a3b3+a2b4,a3a3b3+a3b3(-b3)
Use the power rule aman=am+n to combine exponents.
a4b2+a3b3+a2b4,a3+3b3+a3b3(-b3)
a4b2+a3b3+a2b4,a6b3+a3b3(-b3)
a4b2+a3b3+a2b4,a6b3+a3b3(-b3)
Rewrite using the commutative property of multiplication.
a4b2+a3b3+a2b4,a6b3-a3b3b3
Multiply b3 by b3 by adding the exponents.
Move b3.
a4b2+a3b3+a2b4,a6b3-(a3(b3b3))
Use the power rule aman=am+n to combine exponents.
a4b2+a3b3+a2b4,a6b3-(a3b3+3)
a4b2+a3b3+a2b4,a6b3-(a3b6)
a4b2+a3b3+a2b4,a6b3-a3b6
a4b2+a3b3+a2b4,a6b3-a3b6
Factor out the GCF of a2b2 from a4b2+a3b3+a2b4+a6b3-a3b6.
Factor out the GCF of a2b2 from each term in the polynomial.
Factor out the GCF of a2b2 from the expression a4b2.
a2b2(a2)+a3b3+a2b4+a6b3-a3b6
Factor out the GCF of a2b2 from the expression a3b3.
a2b2(a2)+a2b2(ab)+a2b4+a6b3-a3b6
Factor out the GCF of a2b2 from the expression a2b4.
a2b2(a2)+a2b2(ab)+a2b2(b2)+a6b3-a3b6
Factor out the GCF of a2b2 from the expression a6b3.
a2b2(a2)+a2b2(ab)+a2b2(b2)+a2b2(a4b)-a3b6
Factor out the GCF of a2b2 from the expression -a3b6.
a2b2(a2)+a2b2(ab)+a2b2(b2)+a2b2(a4b)+a2b2(-ab4)
a2b2(a2)+a2b2(ab)+a2b2(b2)+a2b2(a4b)+a2b2(-ab4)
Since all the terms share a common factor of a2b2, it can be factored out of each term.
a2b2(a2+ab+b2+a4b-ab4)
a2b2(a2+ab+b2+a4b-ab4)
The greatest common factor GCF is the term in front of the factored expression.
a2b2
Find the GCF a^2b^2(a^2+ab+b^2) , a^3b^3(a^3-b^3)