Solve 9left(a-bright)left(a+bright)-3left(a-bright)^2

$$9 \left( a-b \right) \left( a+b \right) -3 { \left(a-b \right) }^{ 2 }$$

Evaluate

$$6\left(a-b\right)\left(a+2b\right)$$

Solution Steps

Use the distributive property to multiply 9 by a-b.

$$\left(9a-9b\right)\left(a+b\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 9a-9b by a+b and combine like terms.

$$9a^{2}-9b^{2}-3\left(a-b\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$9a^{2}-9b^{2}-3\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -3 by a^{2}-2ab+b^{2}.

$$9a^{2}-9b^{2}-3a^{2}+6ab-3b^{2}$$

Combine 9a^{2} and -3a^{2} to get 6a^{2}.

$$6a^{2}-9b^{2}+6ab-3b^{2}$$

Combine -9b^{2} and -3b^{2} to get -12b^{2}.

$$6a^{2}-12b^{2}+6ab$$

Expand

$$6a^{2}+6ab-12b^{2}$$

Solution Steps

Use the distributive property to multiply 9 by a-b.

$$\left(9a-9b\right)\left(a+b\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 9a-9b by a+b and combine like terms.

$$9a^{2}-9b^{2}-3\left(a-b\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

$$9a^{2}-9b^{2}-3\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -3 by a^{2}-2ab+b^{2}.

$$9a^{2}-9b^{2}-3a^{2}+6ab-3b^{2}$$

Combine 9a^{2} and -3a^{2} to get 6a^{2}.

$$6a^{2}-9b^{2}+6ab-3b^{2}$$

Combine -9b^{2} and -3b^{2} to get -12b^{2}.

$$6a^{2}-12b^{2}+6ab$$