What is (30a^6b^{10}+12a^4b^6-9a^{10}b^4)/(3ab) ?

The solution to (30a^6b^{10}+12a^4b^6-9a^{10}b^4)/(3ab) is a^3b^3(10a^2b^6+4b^2-3a^6)

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simplify (30a^6b^{10}+12a^4b^6-9a^{10}b^4)/(3ab)

simplify

\frac{30 a ^{6} b ^{10} + 12 a ^{4} b ^{6} - 9 a ^{10} b ^{4}}{3 ab}

a^{3} b^{3} (10 a^{2} b^{6} + 4 b^{2} - 3 a^{6})

Solution steps

\frac{30 a ^{6} b ^{10} + 12 a ^{4} b ^{6} - 9 a ^{10} b ^{4}}{3 ab}

Factor

30 a^{6} b^{10} + 12 a^{4} b^{6} - 9 a^{10} b^{4} : 3 a^{4} b^{4} (10 a^{2} b^{6} + 4 b^{2} - 3 a^{6})

= \frac{3 a ^{4} b ^{4} ( 10 a ^{2} b ^{6} + 4 b ^{2} - 3 a ^{6} )}{3 ab}

Cancel the common factor:

3

= \frac{a ^{4} b ^{4} ( 10 a ^{2} b ^{6} + 4 b ^{2} - 3 a ^{6} )}{ab}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

a^{4} = a a^{3}

= \frac{a a ^{3} b ^{4} ( 10 a ^{2} b ^{6} + 4 b ^{2} - 3 a ^{6} )}{ab}

Cancel the common factor:

a

= \frac{a ^{3} b ^{4} ( 10 a ^{2} b ^{6} + 4 b ^{2} - 3 a ^{6} )}{b}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

b^{4} = b b^{3}

= \frac{a ^{3} b b ^{3} ( 10 a ^{2} b ^{6} + 4 b ^{2} - 3 a ^{6} )}{b}

Cancel the common factor:

b

= a^{3} b^{3} (10 a^{2} b^{6} + 4 b^{2} - 3 a^{6})

\frac{8 - x}{8 + x}

3 x^{2} + 15 x - 18

\frac{16 m ^{2} - 4 m - 6}{4 m + 2}

2 a + [a - (a + b)]

\frac{32}{72}

What is (30a^6b^{10}+12a^4b^6-9a^{10}b^4)/(3ab) ?
The solution to (30a^6b^{10}+12a^4b^6-9a^{10}b^4)/(3ab) is a^3b^3(10a^2b^6+4b^2-3a^6)