10a+8-3a2a2-a-12⋅9a3-81a3a2-7a-6

Reorder terms.

-3a2+10a+8a2-a-12⋅9a3-81a3a2-7a-6

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-3⋅8=-24 and whose sum is b=10.

Factor 10 out of 10a.

-3a2+10(a)+8a2-a-12⋅9a3-81a3a2-7a-6

Rewrite 10 as -2 plus 12

-3a2+(-2+12)a+8a2-a-12⋅9a3-81a3a2-7a-6

Apply the distributive property.

-3a2-2a+12a+8a2-a-12⋅9a3-81a3a2-7a-6

-3a2-2a+12a+8a2-a-12⋅9a3-81a3a2-7a-6

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-3a2-2a)+12a+8a2-a-12⋅9a3-81a3a2-7a-6

Factor out the greatest common factor (GCF) from each group.

a(-3a-2)-4(-3a-2)a2-a-12⋅9a3-81a3a2-7a-6

a(-3a-2)-4(-3a-2)a2-a-12⋅9a3-81a3a2-7a-6

Factor the polynomial by factoring out the greatest common factor, -3a-2.

(-3a-2)(a-4)a2-a-12⋅9a3-81a3a2-7a-6

(-3a-2)(a-4)a2-a-12⋅9a3-81a3a2-7a-6

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 -1.

-4,3

Write the factored form using these integers.

(-3a-2)(a-4)(a-4)(a+3)⋅9a3-81a3a2-7a-6

(-3a-2)(a-4)(a-4)(a+3)⋅9a3-81a3a2-7a-6

Factor 9a out of 9a3-81a.

Factor 9a out of 9a3.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a2)-81a3a2-7a-6

Factor 9a out of -81a.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a2)+9a(-9)3a2-7a-6

Factor 9a out of 9a(a2)+9a(-9).

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a2-9)3a2-7a-6

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a2-9)3a2-7a-6

Rewrite 9 as 32.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a2-32)3a2-7a-6

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=3.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2-7a-6

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2-7a-6

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-6=-18 and whose sum is b=-7.

Factor -7 out of -7a.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2-7(a)-6

Rewrite -7 as 2 plus -9

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2+(2-9)a-6

Apply the distributive property.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2+2a-9a-6

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)3a2+2a-9a-6

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)(3a2+2a)-9a-6

Factor out the greatest common factor (GCF) from each group.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)a(3a+2)-3(3a+2)

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)a(3a+2)-3(3a+2)

Factor the polynomial by factoring out the greatest common factor, 3a+2.

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)(3a+2)(a-3)

(-3a-2)(a-4)(a-4)(a+3)⋅9a(a+3)(a-3)(3a+2)(a-3)

Factor a+3 out of (a-4)(a+3).

(-3a-2)(a-4)(a+3)(a-4)⋅9a(a+3)(a-3)(3a+2)(a-3)

Factor a+3 out of 9a(a+3)(a-3).

(-3a-2)(a-4)(a+3)(a-4)⋅(a+3)(9a(a-3))(3a+2)(a-3)

Cancel the common factor.

(-3a-2)(a-4)(a+3)(a-4)⋅(a+3)(9a(a-3))(3a+2)(a-3)

Rewrite the expression.

(-3a-2)(a-4)a-4⋅9a(a-3)(3a+2)(a-3)

(-3a-2)(a-4)a-4⋅9a(a-3)(3a+2)(a-3)

Multiply (-3a-2)(a-4)a-4 and 9a(a-3)(3a+2)(a-3).

(-3a-2)(a-4)(9a(a-3))(a-4)((3a+2)(a-3))

Factor -1 out of -3a.

(-(3a)-2)(a-4)(9a(a-3))(a-4)((3a+2)(a-3))

Rewrite -2 as -1(2).

(-(3a)-1(2))(a-4)(9a(a-3))(a-4)((3a+2)(a-3))

Factor -1 out of -(3a)-1(2).

-(3a+2)(a-4)(9a(a-3))(a-4)((3a+2)(a-3))

Rewrite -(3a+2) as -1(3a+2).

-1(3a+2)(a-4)(9a(a-3))(a-4)((3a+2)(a-3))

Cancel the common factor.

-1(3a+2)(a-4)⋅9a(a-3)(a-4)(3a+2)(a-3)

Rewrite the expression.

(-1(a-4))⋅9a(a-3)(a-4)(a-3)

(-1(a-4))⋅9a(a-3)(a-4)(a-3)

Cancel the common factor.

-1(a-4)⋅9a(a-3)(a-4)(a-3)

Rewrite the expression.

(-1)⋅9a(a-3)a-3

(-1)⋅9a(a-3)a-3

Cancel the common factor.

(-1)⋅9a(a-3)a-3

Divide (-1)⋅9a by 1.

(-1)⋅9a

(-1)⋅9a

Multiply -1 by 9.

-9a

Simplify (10a+8-3a^2)/(a^2-a-12)*(9a^3-81a)/(3a^2-7a-6)