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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+4\right)^{2}.

$$\left(25x^{2}+40x+16\right)\left(x+2\right)+\left(5x+4\right)\left(x+2\right)$$

Use the distributive property to multiply 25x^{2}+40x+16 by x+2 and combine like terms.

$$25x^{3}+90x^{2}+96x+32+\left(5x+4\right)\left(x+2\right)$$

Use the distributive property to multiply 5x+4 by x+2 and combine like terms.

$$25x^{3}+90x^{2}+96x+32+5x^{2}+14x+8$$

Combine 90x^{2} and 5x^{2} to get 95x^{2}.

$$25x^{3}+95x^{2}+96x+32+14x+8$$

Combine 96x and 14x to get 110x.

$$25x^{3}+95x^{2}+110x+32+8$$

Add 32 and 8 to get 40.

$$25x^{3}+95x^{2}+110x+40$$

Expand

$$25x^{3}+95x^{2}+110x+40$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+4\right)^{2}.

$$\left(25x^{2}+40x+16\right)\left(x+2\right)+\left(5x+4\right)\left(x+2\right)$$

Use the distributive property to multiply 25x^{2}+40x+16 by x+2 and combine like terms.

$$25x^{3}+90x^{2}+96x+32+\left(5x+4\right)\left(x+2\right)$$

Use the distributive property to multiply 5x+4 by x+2 and combine like terms.

$$25x^{3}+90x^{2}+96x+32+5x^{2}+14x+8$$

Combine 90x^{2} and 5x^{2} to get 95x^{2}.

$$25x^{3}+95x^{2}+96x+32+14x+8$$

Combine 96x and 14x to get 110x.

$$25x^{3}+95x^{2}+110x+32+8$$

Add 32 and 8 to get 40.

$$25x^{3}+95x^{2}+110x+40$$