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

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

Evaluate

$$-13x^{2}-11x-100$$

Solution Steps

Combine 2x and x to get 3x.

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

Use the distributive property to multiply 5 by 3x+2.

$$2x^{2}-\left(\left(15x+10\right)x+x\right)-4\times 5\times 5$$

Use the distributive property to multiply 15x+10 by x.

$$2x^{2}-\left(15x^{2}+10x+x\right)-4\times 5\times 5$$

Combine 10x and x to get 11x.

$$2x^{2}-\left(15x^{2}+11x\right)-4\times 5\times 5$$

To find the opposite of 15x^{2}+11x, find the opposite of each term.

$$2x^{2}-15x^{2}-11x-4\times 5\times 5$$

Combine 2x^{2} and -15x^{2} to get -13x^{2}.

$$-13x^{2}-11x-4\times 5\times 5$$

Multiply 4 and 5 to get 20.

$$-13x^{2}-11x-20\times 5$$

Multiply 20 and 5 to get 100.

$$-13x^{2}-11x-100$$

Expand

$$-13x^{2}-11x-100$$

Solution Steps

Combine 2x and x to get 3x.

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

Use the distributive property to multiply 5 by 3x+2.

$$2x^{2}-\left(\left(15x+10\right)x+x\right)-4\times 5\times 5$$

Use the distributive property to multiply 15x+10 by x.

$$2x^{2}-\left(15x^{2}+10x+x\right)-4\times 5\times 5$$

Combine 10x and x to get 11x.

$$2x^{2}-\left(15x^{2}+11x\right)-4\times 5\times 5$$

To find the opposite of 15x^{2}+11x, find the opposite of each term.

$$2x^{2}-15x^{2}-11x-4\times 5\times 5$$

Combine 2x^{2} and -15x^{2} to get -13x^{2}.

$$-13x^{2}-11x-4\times 5\times 5$$

Multiply 4 and 5 to get 20.

$$-13x^{2}-11x-20\times 5$$

Multiply 20 and 5 to get 100.

$$-13x^{2}-11x-100$$