# Simplify (a^2-36)/(4a^2+4ab)*(a^2+2a+ab+2b)/(a^2+8a+12) a2-364a2+4ab⋅a2+2a+ab+2ba2+8a+12
Simplify the numerator.
Rewrite 36 as 62.
a2-624a2+4ab⋅a2+2a+ab+2ba2+8a+12
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=6.
(a+6)(a-6)4a2+4ab⋅a2+2a+ab+2ba2+8a+12
(a+6)(a-6)4a2+4ab⋅a2+2a+ab+2ba2+8a+12
Factor 4a out of 4a2+4ab.
Factor 4a out of 4a2.
(a+6)(a-6)4a(a)+4ab⋅a2+2a+ab+2ba2+8a+12
Factor 4a out of 4ab.
(a+6)(a-6)4a(a)+4a(b)⋅a2+2a+ab+2ba2+8a+12
Factor 4a out of 4a(a)+4a(b).
(a+6)(a-6)4a(a+b)⋅a2+2a+ab+2ba2+8a+12
(a+6)(a-6)4a(a+b)⋅a2+2a+ab+2ba2+8a+12
Simplify the numerator.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(a+6)(a-6)4a(a+b)⋅(a2+2a)+ab+2ba2+8a+12
Factor out the greatest common factor (GCF) from each group.
(a+6)(a-6)4a(a+b)⋅a(a+2)+b(a+2)a2+8a+12
(a+6)(a-6)4a(a+b)⋅a(a+2)+b(a+2)a2+8a+12
Factor the polynomial by factoring out the greatest common factor, a+2.
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)a2+8a+12
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)a2+8a+12
Factor a2+8a+12 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 12 and whose sum is 8.
2,6
Write the factored form using these integers.
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)(a+2)(a+6)
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)(a+2)(a+6)
Simplify terms.
Cancel the common factor of a+6.
Factor a+6 out of (a+2)(a+6).
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)(a+6)(a+2)
Cancel the common factor.
(a+6)(a-6)4a(a+b)⋅(a+2)(a+b)(a+6)(a+2)
Rewrite the expression.
a-64a(a+b)⋅(a+2)(a+b)a+2
a-64a(a+b)⋅(a+2)(a+b)a+2
Cancel the common factor of a+b.
Factor a+b out of 4a(a+b).
a-6(a+b)(4a)⋅(a+2)(a+b)a+2
Factor a+b out of (a+2)(a+b).
a-6(a+b)(4a)⋅(a+b)(a+2)a+2
Cancel the common factor.
a-6(a+b)(4a)⋅(a+b)(a+2)a+2
Rewrite the expression.
a-64a⋅a+2a+2
a-64a⋅a+2a+2
Multiply a-64a and a+2a+2.
(a-6)(a+2)4a(a+2)
Cancel the common factor of a+2.
Cancel the common factor.
(a-6)(a+2)4a(a+2)
Rewrite the expression.
a-64a
a-64a
a-64a
Simplify (a^2-36)/(4a^2+4ab)*(a^2+2a+ab+2b)/(a^2+8a+12)     