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

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

Evaluate

$$90y^{2}+24y-7$$

Solution Steps

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

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

Use the distributive property to multiply 3y+4 by 2-3y and combine like terms.

$$81y^{2}+18y+1-\left(-6y-9y^{2}+8\right)$$

To find the opposite of -6y-9y^{2}+8, find the opposite of each term.

$$81y^{2}+18y+1+6y+9y^{2}-8$$

Combine 18y and 6y to get 24y.

$$81y^{2}+24y+1+9y^{2}-8$$

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

$$90y^{2}+24y+1-8$$

Subtract 8 from 1 to get -7.

$$90y^{2}+24y-7$$

Expand

$$90y^{2}+24y-7$$

Solution Steps

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

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

Use the distributive property to multiply 3y+4 by 2-3y and combine like terms.

$$81y^{2}+18y+1-\left(-6y-9y^{2}+8\right)$$

To find the opposite of -6y-9y^{2}+8, find the opposite of each term.

$$81y^{2}+18y+1+6y+9y^{2}-8$$

Combine 18y and 6y to get 24y.

$$81y^{2}+24y+1+9y^{2}-8$$

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

$$90y^{2}+24y+1-8$$

Subtract 8 from 1 to get -7.

$$90y^{2}+24y-7$$