Solve (9y+1)^2-(3y+4)(z-3y)

$$( 9 y + 1 ) ^ { 2 } - ( 3 y + 4 ) ( z - 3 y )$$

Evaluate

$$-\left(z-3y\right)\left(3y+4\right)+\left(9y+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9y+1\right)^{2}.

$$81y^{2}+18y+1-\left(3y+4\right)\left(z-3y\right)$$

Use the distributive property to multiply 3y+4 by z-3y.

$$81y^{2}+18y+1-\left(3yz-9y^{2}+4z-12y\right)$$

To find the opposite of 3yz-9y^{2}+4z-12y, find the opposite of each term.

$$81y^{2}+18y+1-3yz+9y^{2}-4z+12y$$

Combine 81y^{2} and 9y^{2} to get 90y^{2}.

$$90y^{2}+18y+1-3yz-4z+12y$$

Combine 18y and 12y to get 30y.

$$90y^{2}+30y+1-3yz-4z$$

Expand

$$90y^{2}-3yz+30y-4z+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9y+1\right)^{2}.

$$81y^{2}+18y+1-\left(3y+4\right)\left(z-3y\right)$$

Use the distributive property to multiply 3y+4 by z-3y.

$$81y^{2}+18y+1-\left(3yz-9y^{2}+4z-12y\right)$$

To find the opposite of 3yz-9y^{2}+4z-12y, find the opposite of each term.

$$81y^{2}+18y+1-3yz+9y^{2}-4z+12y$$

Combine 81y^{2} and 9y^{2} to get 90y^{2}.

$$90y^{2}+18y+1-3yz-4z+12y$$

Combine 18y and 12y to get 30y.

$$90y^{2}+30y+1-3yz-4z$$