Solve (2a+b)^2-(a-b)^2*[2]

$$( 2 a + b ) ^ { 2 } - ( a - b ) ^ { 2 } \cdot [ 2 ]$$

Evaluate

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

Solution Steps

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

$$4a^{2}+4ab+b^{2}-\left(a-b\right)^{2}\times 2$$

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

$$4a^{2}+4ab+b^{2}-\left(a^{2}-2ab+b^{2}\right)\times 2$$

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

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

To find the opposite of 2a^{2}-4ab+2b^{2}, find the opposite of each term.

$$4a^{2}+4ab+b^{2}-2a^{2}+4ab-2b^{2}$$

Combine 4a^{2} and -2a^{2} to get 2a^{2}.

$$2a^{2}+4ab+b^{2}+4ab-2b^{2}$$

Combine 4ab and 4ab to get 8ab.

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

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

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

Expand

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

Solution Steps

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

$$4a^{2}+4ab+b^{2}-\left(a-b\right)^{2}\times 2$$

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

$$4a^{2}+4ab+b^{2}-\left(a^{2}-2ab+b^{2}\right)\times 2$$

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

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

To find the opposite of 2a^{2}-4ab+2b^{2}, find the opposite of each term.

$$4a^{2}+4ab+b^{2}-2a^{2}+4ab-2b^{2}$$

Combine 4a^{2} and -2a^{2} to get 2a^{2}.

$$2a^{2}+4ab+b^{2}+4ab-2b^{2}$$

Combine 4ab and 4ab to get 8ab.

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

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

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