(2a+2b-c)(2a-2b+c)-এর সমাধান করুন

$$( 2 a + 2 b - c ) ( 2 a - 2 b + c )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 2a+2b-c by each term of 2a-2b+c.

$$4a^{2}-4ab+2ac+4ba-4b^{2}+2bc-2ca+2cb-c^{2}$$

Combine -4ab and 4ba to get 0.

$$4a^{2}+2ac-4b^{2}+2bc-2ca+2cb-c^{2}$$

Combine 2ac and -2ca to get 0.

$$4a^{2}-4b^{2}+2bc+2cb-c^{2}$$

Combine 2bc and 2cb to get 4bc.

$$4a^{2}-4b^{2}+4bc-c^{2}$$

Expand

$$4a^{2}-4b^{2}+4bc-c^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 2a+2b-c by each term of 2a-2b+c.

$$4a^{2}-4ab+2ac+4ba-4b^{2}+2bc-2ca+2cb-c^{2}$$

Combine -4ab and 4ba to get 0.

$$4a^{2}+2ac-4b^{2}+2bc-2ca+2cb-c^{2}$$

Combine 2ac and -2ca to get 0.

$$4a^{2}-4b^{2}+2bc+2cb-c^{2}$$

Combine 2bc and 2cb to get 4bc.

$$4a^{2}-4b^{2}+4bc-c^{2}$$