Solve (ab+1)(ab-a^2b^2)+(a^2b^2-ab)(ab+1)

$$( a b + 1 ) ( a b - a ^ { 2 } b ^ { 2 } ) + ( a ^ { 2 } b ^ { 2 } - a b ) ( a b + 1 )$$

Evaluate

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Solution Steps

Use the distributive property to multiply ab+1 by ab-a^{2}b^{2}.

$$ab\left(ab-a^{2}b^{2}\right)+ab-a^{2}b^{2}+\left(a^{2}b^{2}-ab\right)\left(ab+1\right)$$

Use the distributive property to multiply a^{2}b^{2}-ab by ab+1 and combine like terms.

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

Use the distributive property to multiply ab by ab-a^{2}b^{2}.

$$a^{2}b^{2}-a^{3}b^{3}+ab-a^{2}b^{2}+a^{3}b^{3}-ab$$

Combine a^{2}b^{2} and -a^{2}b^{2} to get 0.

$$-a^{3}b^{3}+ab+a^{3}b^{3}-ab$$

Combine -a^{3}b^{3} and a^{3}b^{3} to get 0.

$$ab-ab$$

Combine ab and -ab to get 0.

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Factor

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Solution Steps

Factor out common term a by using distributive property.

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

Consider b-b^{3}a^{2}-b+b^{3}a^{2}. Simplify.

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