Solve (2a^3-5a^3)(3ab-ab)(2b^2+5b^2)

$$( 2 a ^ { 3 } - 5 a ^ { 3 } ) ( 3 a b - a b ) ( 2 b ^ { 2 } + 5 b ^ { 2 } )$$

Evaluate

$$-42b^{3}a^{4}$$

Solution Steps

Combine 2a^{3} and -5a^{3} to get -3a^{3}.

$$-3a^{3}\left(3ab-ab\right)\left(2b^{2}+5b^{2}\right)$$

Combine 3ab and -ab to get 2ab.

$$-3a^{3}\times 2ab\left(2b^{2}+5b^{2}\right)$$

Multiply -3 and 2 to get -6.

$$-6a^{3}ab\left(2b^{2}+5b^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-6a^{4}b\left(2b^{2}+5b^{2}\right)$$

Combine 2b^{2} and 5b^{2} to get 7b^{2}.

$$-6a^{4}b\times 7b^{2}$$

Multiply -6 and 7 to get -42.

$$-42a^{4}bb^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-42a^{4}b^{3}$$

Expand

$$-42b^{3}a^{4}$$

Solution Steps

Combine 2a^{3} and -5a^{3} to get -3a^{3}.

$$-3a^{3}\left(3ab-ab\right)\left(2b^{2}+5b^{2}\right)$$

Combine 3ab and -ab to get 2ab.

$$-3a^{3}\times 2ab\left(2b^{2}+5b^{2}\right)$$

Multiply -3 and 2 to get -6.

$$-6a^{3}ab\left(2b^{2}+5b^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-6a^{4}b\left(2b^{2}+5b^{2}\right)$$

Combine 2b^{2} and 5b^{2} to get 7b^{2}.

$$-6a^{4}b\times 7b^{2}$$

Multiply -6 and 7 to get -42.

$$-42a^{4}bb^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-42a^{4}b^{3}$$