Solve (x-3y)(x^2+3xy+9y^2)-(3y+x)

$$( x - 3 y ) ( x ^ { 2 } + 3 x y + 9 y ^ { 2 } ) - ( 3 y + x )$$

Evaluate

$$x^{3}-x-27y^{3}-3y$$

Solution Steps

Use the distributive property to multiply x-3y by x^{2}+3xy+9y^{2} and combine like terms.

$$x^{3}-27y^{3}-\left(3y+x\right)$$

To find the opposite of 3y+x, find the opposite of each term.

$$x^{3}-27y^{3}-3y-x$$

Expand

$$x^{3}-x-27y^{3}-3y$$

Solution Steps

Use the distributive property to multiply x-3y by x^{2}+3xy+9y^{2} and combine like terms.

$$x^{3}-27y^{3}-\left(3y+x\right)$$

To find the opposite of 3y+x, find the opposite of each term.

$$x^{3}-27y^{3}-3y-x$$