Solve 3(d-2)(d+3)+(d-4)^2

$$3 ( d - 2 ) ( d + 3 ) + ( d - 4 ) ^ { 2 }$$

Evaluate

$$4d^{2}-5d-2$$

Solution Steps

Use the distributive property to multiply 3 by d-2.

$$\left(3d-6\right)\left(d+3\right)+\left(d-4\right)^{2}$$

Use the distributive property to multiply 3d-6 by d+3 and combine like terms.

$$3d^{2}+3d-18+\left(d-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(d-4\right)^{2}.

$$3d^{2}+3d-18+d^{2}-8d+16$$

Combine 3d^{2} and d^{2} to get 4d^{2}.

$$4d^{2}+3d-18-8d+16$$

Combine 3d and -8d to get -5d.

$$4d^{2}-5d-18+16$$

Add -18 and 16 to get -2.

$$4d^{2}-5d-2$$

Expand

$$4d^{2}-5d-2$$

Solution Steps

Use the distributive property to multiply 3 by d-2.

$$\left(3d-6\right)\left(d+3\right)+\left(d-4\right)^{2}$$

Use the distributive property to multiply 3d-6 by d+3 and combine like terms.

$$3d^{2}+3d-18+\left(d-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(d-4\right)^{2}.

$$3d^{2}+3d-18+d^{2}-8d+16$$

Combine 3d^{2} and d^{2} to get 4d^{2}.

$$4d^{2}+3d-18-8d+16$$

Combine 3d and -8d to get -5d.

$$4d^{2}-5d-18+16$$

Add -18 and 16 to get -2.

$$4d^{2}-5d-2$$