Solve B(x)=(5x+4)^2-2(5x+4)(7-2x)

$$B ( x ) = ( 5 x + 4 ) ^ { 2 } - 2 ( 5 x + 4 ) ( 7 - 2 x )$$

Evaluate

$$\left(9x-10\right)\left(5x+4\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+4\right)^{2}.

$$25x^{2}+40x+16-2\left(5x+4\right)\left(7-2x\right)$$

Use the distributive property to multiply -2 by 5x+4.

$$25x^{2}+40x+16+\left(-10x-8\right)\left(7-2x\right)$$

Use the distributive property to multiply -10x-8 by 7-2x and combine like terms.

$$25x^{2}+40x+16-54x+20x^{2}-56$$

Combine 40x and -54x to get -14x.

$$25x^{2}-14x+16+20x^{2}-56$$

Combine 25x^{2} and 20x^{2} to get 45x^{2}.

$$45x^{2}-14x+16-56$$

Subtract 56 from 16 to get -40.

$$45x^{2}-14x-40$$

Expand

$$45x^{2}-14x-40$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+4\right)^{2}.

$$25x^{2}+40x+16-2\left(5x+4\right)\left(7-2x\right)$$

Use the distributive property to multiply -2 by 5x+4.

$$25x^{2}+40x+16+\left(-10x-8\right)\left(7-2x\right)$$

Use the distributive property to multiply -10x-8 by 7-2x and combine like terms.

$$25x^{2}+40x+16-54x+20x^{2}-56$$

Combine 40x and -54x to get -14x.

$$25x^{2}-14x+16+20x^{2}-56$$

Combine 25x^{2} and 20x^{2} to get 45x^{2}.

$$45x^{2}-14x+16-56$$

Subtract 56 from 16 to get -40.

$$45x^{2}-14x-40$$