Solve (2x-5)^2-(4x-10)(x-2)+4x^2+25

$$( 2 x - 5 ) ^ { 2 } - ( 4 x - 10 ) ( x - 2 ) + 4 x ^ { 2 } + 25$$

Evaluate

$$4x^{2}-2x+30$$

Solution Steps

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

$$4x^{2}-20x+25-\left(4x-10\right)\left(x-2\right)+4x^{2}+25$$

Use the distributive property to multiply 4x-10 by x-2 and combine like terms.

$$4x^{2}-20x+25-\left(4x^{2}-18x+20\right)+4x^{2}+25$$

To find the opposite of 4x^{2}-18x+20, find the opposite of each term.

$$4x^{2}-20x+25-4x^{2}+18x-20+4x^{2}+25$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-20x+25+18x-20+4x^{2}+25$$

Combine -20x and 18x to get -2x.

$$-2x+25-20+4x^{2}+25$$

Subtract 20 from 25 to get 5.

$$-2x+5+4x^{2}+25$$

Add 5 and 25 to get 30.

$$-2x+30+4x^{2}$$

Expand

$$4x^{2}-2x+30$$

Solution Steps

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

$$4x^{2}-20x+25-\left(4x-10\right)\left(x-2\right)+4x^{2}+25$$

Use the distributive property to multiply 4x-10 by x-2 and combine like terms.

$$4x^{2}-20x+25-\left(4x^{2}-18x+20\right)+4x^{2}+25$$

To find the opposite of 4x^{2}-18x+20, find the opposite of each term.

$$4x^{2}-20x+25-4x^{2}+18x-20+4x^{2}+25$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-20x+25+18x-20+4x^{2}+25$$

Combine -20x and 18x to get -2x.

$$-2x+25-20+4x^{2}+25$$

Subtract 20 from 25 to get 5.

$$-2x+5+4x^{2}+25$$

Add 5 and 25 to get 30.

$$-2x+30+4x^{2}$$