Solve (2x-b)(3x+b)+(3b-x)(b+x)

$$( 2 x - b ) ( 3 x + b ) + ( 3 b - x ) ( b + x )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 2x-b by each term of 3x+b.

$$6x^{2}+2xb-3bx-b^{2}+\left(3b-x\right)\left(b+x\right)$$

Combine 2xb and -3bx to get -xb.

$$6x^{2}-xb-b^{2}+\left(3b-x\right)\left(b+x\right)$$

Apply the distributive property by multiplying each term of 3b-x by each term of b+x.

$$6x^{2}-xb-b^{2}+3b^{2}+3bx-xb-x^{2}$$

Combine 3bx and -xb to get 2bx.

$$6x^{2}-xb-b^{2}+3b^{2}+2bx-x^{2}$$

Combine -b^{2} and 3b^{2} to get 2b^{2}.

$$6x^{2}-xb+2b^{2}+2bx-x^{2}$$

Combine -xb and 2bx to get xb.

$$6x^{2}+xb+2b^{2}-x^{2}$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of 2x-b by each term of 3x+b.

$$6x^{2}+2xb-3bx-b^{2}+\left(3b-x\right)\left(b+x\right)$$

Combine 2xb and -3bx to get -xb.

$$6x^{2}-xb-b^{2}+\left(3b-x\right)\left(b+x\right)$$

Apply the distributive property by multiplying each term of 3b-x by each term of b+x.

$$6x^{2}-xb-b^{2}+3b^{2}+3bx-xb-x^{2}$$

Combine 3bx and -xb to get 2bx.

$$6x^{2}-xb-b^{2}+3b^{2}+2bx-x^{2}$$

Combine -b^{2} and 3b^{2} to get 2b^{2}.

$$6x^{2}-xb+2b^{2}+2bx-x^{2}$$

Combine -xb and 2bx to get xb.

$$6x^{2}+xb+2b^{2}-x^{2}$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

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