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

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

Evaluate

$$a^{2}-12ab+57b^{2}$$

Solution Steps

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

$$4a^{2}-12ab+9b^{2}-3\left(a+4b\right)\left(a-4b\right)$$

Use the distributive property to multiply -3 by a+4b.

$$4a^{2}-12ab+9b^{2}+\left(-3a-12b\right)\left(a-4b\right)$$

Use the distributive property to multiply -3a-12b by a-4b and combine like terms.

$$4a^{2}-12ab+9b^{2}-3a^{2}+48b^{2}$$

Combine 4a^{2} and -3a^{2} to get a^{2}.

$$a^{2}-12ab+9b^{2}+48b^{2}$$

Combine 9b^{2} and 48b^{2} to get 57b^{2}.

$$a^{2}-12ab+57b^{2}$$

Expand

$$a^{2}-12ab+57b^{2}$$

Solution Steps

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

$$4a^{2}-12ab+9b^{2}-3\left(a+4b\right)\left(a-4b\right)$$

Use the distributive property to multiply -3 by a+4b.

$$4a^{2}-12ab+9b^{2}+\left(-3a-12b\right)\left(a-4b\right)$$

Use the distributive property to multiply -3a-12b by a-4b and combine like terms.

$$4a^{2}-12ab+9b^{2}-3a^{2}+48b^{2}$$

Combine 4a^{2} and -3a^{2} to get a^{2}.

$$a^{2}-12ab+9b^{2}+48b^{2}$$

Combine 9b^{2} and 48b^{2} to get 57b^{2}.

$$a^{2}-12ab+57b^{2}$$