Solve 5(2x+1)^2+(5x-6)*2(2x+1)*2

$$5 ( 2 x + 1 ) ^ { 2 } + ( 5 x - 6 ) \cdot 2 ( 2 x + 1 ) \cdot 2$$

Evaluate

$$\left(30x-19\right)\left(2x+1\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$5\left(4x^{2}+4x+1\right)+\left(5x-6\right)\times 2\left(2x+1\right)\times 2$$

Use the distributive property to multiply 5 by 4x^{2}+4x+1.

$$20x^{2}+20x+5+\left(5x-6\right)\times 2\left(2x+1\right)\times 2$$

Multiply 2 and 2 to get 4.

$$20x^{2}+20x+5+\left(5x-6\right)\times 4\left(2x+1\right)$$

Use the distributive property to multiply 5x-6 by 4.

$$20x^{2}+20x+5+\left(20x-24\right)\left(2x+1\right)$$

Use the distributive property to multiply 20x-24 by 2x+1 and combine like terms.

$$20x^{2}+20x+5+40x^{2}-28x-24$$

Combine 20x^{2} and 40x^{2} to get 60x^{2}.

$$60x^{2}+20x+5-28x-24$$

Combine 20x and -28x to get -8x.

$$60x^{2}-8x+5-24$$

Subtract 24 from 5 to get -19.

$$60x^{2}-8x-19$$

Expand

$$60x^{2}-8x-19$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$5\left(4x^{2}+4x+1\right)+\left(5x-6\right)\times 2\left(2x+1\right)\times 2$$

Use the distributive property to multiply 5 by 4x^{2}+4x+1.

$$20x^{2}+20x+5+\left(5x-6\right)\times 2\left(2x+1\right)\times 2$$

Multiply 2 and 2 to get 4.

$$20x^{2}+20x+5+\left(5x-6\right)\times 4\left(2x+1\right)$$

Use the distributive property to multiply 5x-6 by 4.

$$20x^{2}+20x+5+\left(20x-24\right)\left(2x+1\right)$$

Use the distributive property to multiply 20x-24 by 2x+1 and combine like terms.

$$20x^{2}+20x+5+40x^{2}-28x-24$$

Combine 20x^{2} and 40x^{2} to get 60x^{2}.

$$60x^{2}+20x+5-28x-24$$

Combine 20x and -28x to get -8x.

$$60x^{2}-8x+5-24$$

Subtract 24 from 5 to get -19.

$$60x^{2}-8x-19$$