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

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

Evaluate

$$15x+19$$

Solution Steps

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

$$x^{2}+10x+25-\left(x-2\right)\left(x-3\right)$$

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

$$x^{2}+10x+25-\left(x^{2}-5x+6\right)$$

To find the opposite of x^{2}-5x+6, find the opposite of each term.

$$x^{2}+10x+25-x^{2}+5x-6$$

Combine x^{2} and -x^{2} to get 0.

$$10x+25+5x-6$$

Combine 10x and 5x to get 15x.

$$15x+25-6$$

Subtract 6 from 25 to get 19.

$$15x+19$$

Expand

$$15x+19$$

Solution Steps

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

$$x^{2}+10x+25-\left(x-2\right)\left(x-3\right)$$

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

$$x^{2}+10x+25-\left(x^{2}-5x+6\right)$$

To find the opposite of x^{2}-5x+6, find the opposite of each term.

$$x^{2}+10x+25-x^{2}+5x-6$$

Combine x^{2} and -x^{2} to get 0.

$$10x+25+5x-6$$

Combine 10x and 5x to get 15x.

$$15x+25-6$$

Subtract 6 from 25 to get 19.

$$15x+19$$