Solve left(2x-3right)^2-(3-2x)(x+5)

$${ \left(2x-3 \right) }^{ 2 } -(3-2x)(x+5)$$

Evaluate

$$\left(2x-3\right)\left(3x+2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9-\left(3-2x\right)\left(x+5\right)$$

Use the distributive property to multiply 3-2x by x+5 and combine like terms.

$$4x^{2}-12x+9-\left(-7x+15-2x^{2}\right)$$

To find the opposite of -7x+15-2x^{2}, find the opposite of each term.

$$4x^{2}-12x+9+7x-15+2x^{2}$$

Combine -12x and 7x to get -5x.

$$4x^{2}-5x+9-15+2x^{2}$$

Subtract 15 from 9 to get -6.

$$4x^{2}-5x-6+2x^{2}$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}-5x-6$$

Expand

$$6x^{2}-5x-6$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9-\left(3-2x\right)\left(x+5\right)$$

Use the distributive property to multiply 3-2x by x+5 and combine like terms.

$$4x^{2}-12x+9-\left(-7x+15-2x^{2}\right)$$

To find the opposite of -7x+15-2x^{2}, find the opposite of each term.

$$4x^{2}-12x+9+7x-15+2x^{2}$$

Combine -12x and 7x to get -5x.

$$4x^{2}-5x+9-15+2x^{2}$$

Subtract 15 from 9 to get -6.

$$4x^{2}-5x-6+2x^{2}$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}-5x-6$$