Solve (2a-b)(b+3b)-4(b-2a)^2

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

Evaluate

$$8\left(b-a\right)\left(2a-b\right)$$

Solution Steps

Combine b and 3b to get 4b.

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

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

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

Use the distributive property to multiply 8a-4b by b.

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

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

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

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

$$8ab-4b^{2}-4b^{2}+16ba-16a^{2}$$

Combine -4b^{2} and -4b^{2} to get -8b^{2}.

$$8ab-8b^{2}+16ba-16a^{2}$$

Combine 8ab and 16ba to get 24ab.

$$24ab-8b^{2}-16a^{2}$$

Expand

$$-16a^{2}+24ab-8b^{2}$$

Solution Steps

Combine b and 3b to get 4b.

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

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

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

Use the distributive property to multiply 8a-4b by b.

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

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

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

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

$$8ab-4b^{2}-4b^{2}+16ba-16a^{2}$$

Combine -4b^{2} and -4b^{2} to get -8b^{2}.

$$8ab-8b^{2}+16ba-16a^{2}$$

Combine 8ab and 16ba to get 24ab.

$$24ab-8b^{2}-16a^{2}$$