Solve (3a-b)^2-(a+b)(3a-b)=

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

Evaluate

$$2\left(a-b\right)\left(3a-b\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-b\right)^{2}.

$$9a^{2}-6ab+b^{2}-\left(a+b\right)\left(3a-b\right)$$

Use the distributive property to multiply a+b by 3a-b and combine like terms.

$$9a^{2}-6ab+b^{2}-\left(3a^{2}+2ab-b^{2}\right)$$

To find the opposite of 3a^{2}+2ab-b^{2}, find the opposite of each term.

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

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

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

Combine -6ab and -2ab to get -8ab.

$$6a^{2}-8ab+b^{2}+b^{2}$$

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

$$6a^{2}-8ab+2b^{2}$$

Expand

$$6a^{2}-8ab+2b^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-b\right)^{2}.

$$9a^{2}-6ab+b^{2}-\left(a+b\right)\left(3a-b\right)$$

Use the distributive property to multiply a+b by 3a-b and combine like terms.

$$9a^{2}-6ab+b^{2}-\left(3a^{2}+2ab-b^{2}\right)$$

To find the opposite of 3a^{2}+2ab-b^{2}, find the opposite of each term.

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

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

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

Combine -6ab and -2ab to get -8ab.

$$6a^{2}-8ab+b^{2}+b^{2}$$

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

$$6a^{2}-8ab+2b^{2}$$