Solve 2^2((1-p)^2)+(-2^2(p-p^2))=

$$2 ^ { 2 } ( ( 1 - p ) ^ { 2 } ) + ( - 2 ^ { 2 } ( p - p ^ { 2 } ) ) =$$

Evaluate

$$4\left(p-1\right)\left(2p-1\right)$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

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

$$4-8p+4p^{2}+\left(-2^{2}\right)\left(p-p^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$4-8p+4p^{2}-4\left(p-p^{2}\right)$$

Use the distributive property to multiply -4 by p-p^{2}.

$$4-8p+4p^{2}-4p+4p^{2}$$

Combine -8p and -4p to get -12p.

$$4-12p+4p^{2}+4p^{2}$$

Combine 4p^{2} and 4p^{2} to get 8p^{2}.

$$4-12p+8p^{2}$$

Expand

$$8p^{2}-12p+4$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

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

$$4-8p+4p^{2}+\left(-2^{2}\right)\left(p-p^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$4-8p+4p^{2}-4\left(p-p^{2}\right)$$

Use the distributive property to multiply -4 by p-p^{2}.

$$4-8p+4p^{2}-4p+4p^{2}$$

Combine -8p and -4p to get -12p.

$$4-12p+4p^{2}+4p^{2}$$

Combine 4p^{2} and 4p^{2} to get 8p^{2}.

$$4-12p+8p^{2}$$