Simplify (6b^6-15b^4a^2+9b^2a^4)/(-3a^2b^2)

Math
6b6-15b4a2+9b2a4-3a2b2
Simplify the numerator.
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Factor 3b2 out of 6b6-15b4a2+9b2a4.
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Factor 3b2 out of 6b6.
3b2(2b4)-15b4a2+9b2a4-3a2b2
Factor 3b2 out of -15b4a2.
3b2(2b4)+3b2(-5b2a2)+9b2a4-3a2b2
Factor 3b2 out of 9b2a4.
3b2(2b4)+3b2(-5b2a2)+3b2(3a4)-3a2b2
Factor 3b2 out of 3b2(2b4)+3b2(-5b2a2).
3b2(2b4-5b2a2)+3b2(3a4)-3a2b2
Factor 3b2 out of 3b2(2b4-5b2a2)+3b2(3a4).
3b2(2b4-5b2a2+3a4)-3a2b2
3b2(2b4-5b2a2+3a4)-3a2b2
Factor by grouping.
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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⋅2=6 and whose sum is b=-5.
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Reorder terms.
3b2(3a4+2b4-5a2b2)-3a2b2
Reorder 2b4 and -5a2b2.
3b2(3a4-5a2b2+2b4)-3a2b2
Factor -5 out of -5a2b2.
3b2(3a4-5(a2b2)+2b4)-3a2b2
Rewrite -5 as -2 plus -3
3b2(3a4+(-2-3)(a2b2)+2b4)-3a2b2
Apply the distributive property.
3b2(3a4-2(a2b2)-3(a2b2)+2b4)-3a2b2
Move parentheses.
3b2(3a4-2a2b2-3a2b2+2b4)-3a2b2
3b2(3a4-2a2b2-3a2b2+2b4)-3a2b2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
3b2((3a4-2a2b2)-3a2b2+2b4)-3a2b2
Factor out the greatest common factor (GCF) from each group.
3b2(a2(3a2-2b2)-b2(3a2-2b2))-3a2b2
3b2(a2(3a2-2b2)-b2(3a2-2b2))-3a2b2
Factor the polynomial by factoring out the greatest common factor, 3a2-2b2.
3b2((3a2-2b2)(a2-b2))-3a2b2
3b2((3a2-2b2)(a2-b2))-3a2b2
Factor.
3b2(3a2-2b2)(a+b)(a-b)-3a2b2
3b2(3a2-2b2)(a+b)(a-b)-3a2b2
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 3 and -3.
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Factor 3 out of 3b2(3a2-2b2)(a+b)(a-b).
3(((b2(3a2-2b2))(a+b))(a-b))-3a2b2
Cancel the common factors.
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Factor 3 out of -3a2b2.
3(((b2(3a2-2b2))(a+b))(a-b))3(-a2b2)
Cancel the common factor.
3(((b2(3a2-2b2))(a+b))(a-b))3(-a2b2)
Rewrite the expression.
((b2(3a2-2b2))(a+b))(a-b)-a2b2
((b2(3a2-2b2))(a+b))(a-b)-a2b2
((b2(3a2-2b2))(a+b))(a-b)-a2b2
Cancel the common factor of b2.
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Cancel the common factor.
b2(3a2-2b2)(a+b)(a-b)-a2b2
Rewrite the expression.
((3a2-2b2)(a+b))(a-b)-a2
((3a2-2b2)(a+b))(a-b)-a2
Move the negative in front of the fraction.
-(3a2-2b2)(a+b)(a-b)a2
-(3a2-2b2)(a+b)(a-b)a2
Simplify (6b^6-15b^4a^2+9b^2a^4)/(-3a^2b^2)

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