Solve 2(c-d)+6c(d-c)-8(c-d)^2

$$2 ( c - d ) + 6 c ( d - c ) - 8 ( c - d ) ^ { 2 }$$

Evaluate

$$2\left(d-c\right)\left(7c-4d-1\right)$$

Solution Steps

Use the distributive property to multiply 2 by c-d.

$$2c-2d+6c\left(d-c\right)-8\left(c-d\right)^{2}$$

Use the distributive property to multiply 6c by d-c.

$$2c-2d+6cd-6c^{2}-8\left(c-d\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(c-d\right)^{2}.

$$2c-2d+6cd-6c^{2}-8\left(c^{2}-2cd+d^{2}\right)$$

Use the distributive property to multiply -8 by c^{2}-2cd+d^{2}.

$$2c-2d+6cd-6c^{2}-8c^{2}+16cd-8d^{2}$$

Combine -6c^{2} and -8c^{2} to get -14c^{2}.

$$2c-2d+6cd-14c^{2}+16cd-8d^{2}$$

Combine 6cd and 16cd to get 22cd.

$$2c-2d+22cd-14c^{2}-8d^{2}$$

Expand

$$-14c^{2}+22cd+2c-8d^{2}-2d$$

Solution Steps

Use the distributive property to multiply 2 by c-d.

$$2c-2d+6c\left(d-c\right)-8\left(c-d\right)^{2}$$

Use the distributive property to multiply 6c by d-c.

$$2c-2d+6cd-6c^{2}-8\left(c-d\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(c-d\right)^{2}.

$$2c-2d+6cd-6c^{2}-8\left(c^{2}-2cd+d^{2}\right)$$

Use the distributive property to multiply -8 by c^{2}-2cd+d^{2}.

$$2c-2d+6cd-6c^{2}-8c^{2}+16cd-8d^{2}$$

Combine -6c^{2} and -8c^{2} to get -14c^{2}.

$$2c-2d+6cd-14c^{2}+16cd-8d^{2}$$

Combine 6cd and 16cd to get 22cd.

$$2c-2d+22cd-14c^{2}-8d^{2}$$