Solve (5y+1)^2-4(y-1)^2=

$$( 5 y + 1 ) ^ { 2 } - 4 ( y - 1 ) ^ { 2 } =$$

Evaluate

$$3\left(7y-1\right)\left(y+1\right)$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by y^{2}-2y+1.

$$25y^{2}+10y+1-4y^{2}+8y-4$$

Combine 25y^{2} and -4y^{2} to get 21y^{2}.

$$21y^{2}+10y+1+8y-4$$

Combine 10y and 8y to get 18y.

$$21y^{2}+18y+1-4$$

Subtract 4 from 1 to get -3.

$$21y^{2}+18y-3$$

Expand

$$21y^{2}+18y-3$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by y^{2}-2y+1.

$$25y^{2}+10y+1-4y^{2}+8y-4$$

Combine 25y^{2} and -4y^{2} to get 21y^{2}.

$$21y^{2}+10y+1+8y-4$$

Combine 10y and 8y to get 18y.

$$21y^{2}+18y+1-4$$

Subtract 4 from 1 to get -3.

$$21y^{2}+18y-3$$