Solve 5(2x+7)^2+(5x-6)*2(2x+1)x

$$5 ( 2 x + 7 ) ^ { 2 } + ( 5 x - 6 ) \cdot 2 ( 2 x + 1 ) x$$

Evaluate

$$20x^{3}+6x^{2}+128x+245$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+7\right)^{2}.

$$5\left(4x^{2}+28x+49\right)+\left(5x-6\right)\times 2\left(2x+1\right)x$$

Use the distributive property to multiply 5 by 4x^{2}+28x+49.

$$20x^{2}+140x+245+\left(5x-6\right)\times 2\left(2x+1\right)x$$

Use the distributive property to multiply 5x-6 by 2.

$$20x^{2}+140x+245+\left(10x-12\right)\left(2x+1\right)x$$

Use the distributive property to multiply 10x-12 by 2x+1 and combine like terms.

$$20x^{2}+140x+245+\left(20x^{2}-14x-12\right)x$$

Use the distributive property to multiply 20x^{2}-14x-12 by x.

$$20x^{2}+140x+245+20x^{3}-14x^{2}-12x$$

Combine 20x^{2} and -14x^{2} to get 6x^{2}.

$$6x^{2}+140x+245+20x^{3}-12x$$

Combine 140x and -12x to get 128x.

$$6x^{2}+128x+245+20x^{3}$$

Expand

$$20x^{3}+6x^{2}+128x+245$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+7\right)^{2}.

$$5\left(4x^{2}+28x+49\right)+\left(5x-6\right)\times 2\left(2x+1\right)x$$

Use the distributive property to multiply 5 by 4x^{2}+28x+49.

$$20x^{2}+140x+245+\left(5x-6\right)\times 2\left(2x+1\right)x$$

Use the distributive property to multiply 5x-6 by 2.

$$20x^{2}+140x+245+\left(10x-12\right)\left(2x+1\right)x$$

Use the distributive property to multiply 10x-12 by 2x+1 and combine like terms.

$$20x^{2}+140x+245+\left(20x^{2}-14x-12\right)x$$

Use the distributive property to multiply 20x^{2}-14x-12 by x.

$$20x^{2}+140x+245+20x^{3}-14x^{2}-12x$$

Combine 20x^{2} and -14x^{2} to get 6x^{2}.

$$6x^{2}+140x+245+20x^{3}-12x$$

Combine 140x and -12x to get 128x.

$$6x^{2}+128x+245+20x^{3}$$