Solve 4left(a+bright)^2+4left(a^2-b^2right)-3left(a-bright)^2

$$4 { \left(a+b \right) }^{ 2 } +4 \left( { a }^{ 2 } - { b }^{ 2 } \right) -3 { \left(a-b \right) }^{ 2 }$$

Evaluate

$$\left(5a-b\right)\left(a+3b\right)$$

Solution Steps

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

$$4\left(a^{2}+2ab+b^{2}\right)+4\left(a^{2}-b^{2}\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}+2ab+b^{2}.

$$4a^{2}+8ab+4b^{2}+4\left(a^{2}-b^{2}\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}-b^{2}.

$$4a^{2}+8ab+4b^{2}+4a^{2}-4b^{2}-3\left(a-b\right)^{2}$$

Combine 4a^{2} and 4a^{2} to get 8a^{2}.

$$8a^{2}+8ab+4b^{2}-4b^{2}-3\left(a-b\right)^{2}$$

Combine 4b^{2} and -4b^{2} to get 0.

$$8a^{2}+8ab-3\left(a-b\right)^{2}$$

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

$$8a^{2}+8ab-3\left(a^{2}-2ab+b^{2}\right)$$

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

$$8a^{2}+8ab-3a^{2}+6ab-3b^{2}$$

Combine 8a^{2} and -3a^{2} to get 5a^{2}.

$$5a^{2}+8ab+6ab-3b^{2}$$

Combine 8ab and 6ab to get 14ab.

$$5a^{2}+14ab-3b^{2}$$

Expand

$$5a^{2}+14ab-3b^{2}$$

Solution Steps

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

$$4\left(a^{2}+2ab+b^{2}\right)+4\left(a^{2}-b^{2}\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}+2ab+b^{2}.

$$4a^{2}+8ab+4b^{2}+4\left(a^{2}-b^{2}\right)-3\left(a-b\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}-b^{2}.

$$4a^{2}+8ab+4b^{2}+4a^{2}-4b^{2}-3\left(a-b\right)^{2}$$

Combine 4a^{2} and 4a^{2} to get 8a^{2}.

$$8a^{2}+8ab+4b^{2}-4b^{2}-3\left(a-b\right)^{2}$$

Combine 4b^{2} and -4b^{2} to get 0.

$$8a^{2}+8ab-3\left(a-b\right)^{2}$$

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

$$8a^{2}+8ab-3\left(a^{2}-2ab+b^{2}\right)$$

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

$$8a^{2}+8ab-3a^{2}+6ab-3b^{2}$$

Combine 8a^{2} and -3a^{2} to get 5a^{2}.

$$5a^{2}+8ab+6ab-3b^{2}$$

Combine 8ab and 6ab to get 14ab.

$$5a^{2}+14ab-3b^{2}$$