Solve left(5y+1right)^2-left(3y+4right)left(2-3yright)

$${ \left(5y+1 \right) }^{ 2 } - \left( 3y+4 \right) \left( 2-3y \right)$$

Evaluate

$$34y^{2}+16y-7$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5y+1\right)^{2}.

$$25y^{2}+10y+1-\left(3y+4\right)\left(2-3y\right)$$

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

$$25y^{2}+10y+1-\left(-6y-9y^{2}+8\right)$$

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

$$25y^{2}+10y+1+6y+9y^{2}-8$$

Combine 10y and 6y to get 16y.

$$25y^{2}+16y+1+9y^{2}-8$$

Combine 25y^{2} and 9y^{2} to get 34y^{2}.

$$34y^{2}+16y+1-8$$

Subtract 8 from 1 to get -7.

$$34y^{2}+16y-7$$

Expand

$$34y^{2}+16y-7$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5y+1\right)^{2}.

$$25y^{2}+10y+1-\left(3y+4\right)\left(2-3y\right)$$

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

$$25y^{2}+10y+1-\left(-6y-9y^{2}+8\right)$$

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

$$25y^{2}+10y+1+6y+9y^{2}-8$$

Combine 10y and 6y to get 16y.

$$25y^{2}+16y+1+9y^{2}-8$$

Combine 25y^{2} and 9y^{2} to get 34y^{2}.

$$34y^{2}+16y+1-8$$

Subtract 8 from 1 to get -7.

$$34y^{2}+16y-7$$