Solve 2(x-b)^2+5(x-b)+2

$$2 ( x - b ) ^ { 2 } + 5 ( x - b ) + 2$$

Evaluate

$$\left(x-b+2\right)\left(2x-2b+1\right)$$

Solution Steps

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

$$2\left(x^{2}-2xb+b^{2}\right)+5\left(x-b\right)+2$$

Use the distributive property to multiply 2 by x^{2}-2xb+b^{2}.

$$2x^{2}-4xb+2b^{2}+5\left(x-b\right)+2$$

Use the distributive property to multiply 5 by x-b.

$$2x^{2}-4xb+2b^{2}+5x-5b+2$$

Expand

$$2x^{2}-4bx+5x+2b^{2}-5b+2$$

Solution Steps

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

$$2\left(x^{2}-2xb+b^{2}\right)+5\left(x-b\right)+2$$

Use the distributive property to multiply 2 by x^{2}-2xb+b^{2}.

$$2x^{2}-4xb+2b^{2}+5\left(x-b\right)+2$$

Use the distributive property to multiply 5 by x-b.

$$2x^{2}-4xb+2b^{2}+5x-5b+2$$