Solve 2(x+x)(5x-1)+3x(x-2)(2x+1)=

$$2 ( x + x ) ( 5 x - 1 ) + 3 x ( x - 2 ) ( 2 x + 1 ) =$$

Evaluate

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

Solution Steps

Combine x and x to get 2x.

$$2\times 2x\left(5x-1\right)+3x\left(x-2\right)\left(2x+1\right)$$

Multiply 2 and 2 to get 4.

$$4x\left(5x-1\right)+3x\left(x-2\right)\left(2x+1\right)$$

Use the distributive property to multiply 4x by 5x-1.

$$20x^{2}-4x+3x\left(x-2\right)\left(2x+1\right)$$

Use the distributive property to multiply 3x by x-2.

$$20x^{2}-4x+\left(3x^{2}-6x\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{2}-6x by each term of 2x+1.

$$20x^{2}-4x+6x^{3}+3x^{2}-12x^{2}-6x$$

Combine 3x^{2} and -12x^{2} to get -9x^{2}.

$$20x^{2}-4x+6x^{3}-9x^{2}-6x$$

Combine 20x^{2} and -9x^{2} to get 11x^{2}.

$$11x^{2}-4x+6x^{3}-6x$$

Combine -4x and -6x to get -10x.

$$11x^{2}-10x+6x^{3}$$

Expand

$$6x^{3}+11x^{2}-10x$$

Solution Steps

Combine x and x to get 2x.

$$2\times 2x\left(5x-1\right)+3x\left(x-2\right)\left(2x+1\right)$$

Multiply 2 and 2 to get 4.

$$4x\left(5x-1\right)+3x\left(x-2\right)\left(2x+1\right)$$

Use the distributive property to multiply 4x by 5x-1.

$$20x^{2}-4x+3x\left(x-2\right)\left(2x+1\right)$$

Use the distributive property to multiply 3x by x-2.

$$20x^{2}-4x+\left(3x^{2}-6x\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 3x^{2}-6x by each term of 2x+1.

$$20x^{2}-4x+6x^{3}+3x^{2}-12x^{2}-6x$$

Combine 3x^{2} and -12x^{2} to get -9x^{2}.

$$20x^{2}-4x+6x^{3}-9x^{2}-6x$$

Combine 20x^{2} and -9x^{2} to get 11x^{2}.

$$11x^{2}-4x+6x^{3}-6x$$

Combine -4x and -6x to get -10x.

$$11x^{2}-10x+6x^{3}$$