Solve P=(x+2)(x+6)(x^2+8x+10)-15

$$P = ( x + 2 ) ( x + 6 ) ( x ^ { 2 } + 8 x + 10 ) - 15$$

Solve for P

$$P=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)$$

Solution Steps

Use the distributive property to multiply x+2 by x+6 and combine like terms.

$$P=\left(x^{2}+8x+12\right)\left(x^{2}+8x+10\right)-15$$

Use the distributive property to multiply x^{2}+8x+12 by x^{2}+8x+10 and combine like terms.

$$P=x^{4}+16x^{3}+86x^{2}+176x+120-15$$

Subtract 15 from 120 to get 105.

$$P=x^{4}+16x^{3}+86x^{2}+176x+105$$