Solve (1-2*y)^2*(1+2*y)^2=

$$( 1 - 2 \cdot y ) ^ { 2 } \cdot ( 1 + 2 \cdot y ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$1-8y^{2}+16y^{4}$$

Expand

$$16y^{4}-8y^{2}+1$$

Solution Steps

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

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

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

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

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

$$1-8y^{2}+16y^{4}$$