Solve {l}{(x^2+4x+8)^2}{+3(x^2+4x+8)}{+2}

$$\left. \begin{array} { l } { ( x ^ { 2 } + 4 x + 8 ) ^ { 2 } } \\ { + 3 ( x ^ { 2 } + 4 x + 8 ) } \\ { + 2 } \end{array} \right.$$

Evaluate

$$\left(x^{2}+4x+9\right)\left(x^{2}+4x+10\right)$$

Solution Steps

Square x^{2}+4x+8.

$$x^{4}+8x^{3}+32x^{2}+64x+64+3\left(x^{2}+4x+8\right)+2$$

Use the distributive property to multiply 3 by x^{2}+4x+8.

$$x^{4}+8x^{3}+32x^{2}+64x+64+3x^{2}+12x+24+2$$

Combine 32x^{2} and 3x^{2} to get 35x^{2}.

$$x^{4}+8x^{3}+35x^{2}+64x+64+12x+24+2$$

Combine 64x and 12x to get 76x.

$$x^{4}+8x^{3}+35x^{2}+76x+64+24+2$$

Add 64 and 24 to get 88.

$$x^{4}+8x^{3}+35x^{2}+76x+88+2$$

Add 88 and 2 to get 90.

$$x^{4}+8x^{3}+35x^{2}+76x+90$$

Expand

$$x^{4}+8x^{3}+35x^{2}+76x+90$$

Solution Steps

Square x^{2}+4x+8.

$$x^{4}+8x^{3}+32x^{2}+64x+64+3\left(x^{2}+4x+8\right)+2$$

Use the distributive property to multiply 3 by x^{2}+4x+8.

$$x^{4}+8x^{3}+32x^{2}+64x+64+3x^{2}+12x+24+2$$

Combine 32x^{2} and 3x^{2} to get 35x^{2}.

$$x^{4}+8x^{3}+35x^{2}+64x+64+12x+24+2$$

Combine 64x and 12x to get 76x.

$$x^{4}+8x^{3}+35x^{2}+76x+64+24+2$$

Add 64 and 24 to get 88.

$$x^{4}+8x^{3}+35x^{2}+76x+88+2$$

Add 88 and 2 to get 90.

$$x^{4}+8x^{3}+35x^{2}+76x+90$$