Solve 4(a-b)^2-(2a+b)(-b+2a)

$$4 ( a - b ) ^ { 2 } - ( 2 a + b ) ( - b + 2 a )$$

Evaluate

$$b\left(5b-8a\right)$$

Solution Steps

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

$$4\left(a^{2}-2ab+b^{2}\right)-\left(2a+b\right)\left(-b+2a\right)$$

Use the distributive property to multiply 4 by a^{2}-2ab+b^{2}.

$$4a^{2}-8ab+4b^{2}-\left(2a+b\right)\left(-b+2a\right)$$

Use the distributive property to multiply 2a+b by -b+2a.

$$4a^{2}-8ab+4b^{2}-\left(2a\left(-b\right)+4a^{2}+b\left(-b\right)+2ba\right)$$

To find the opposite of 2a\left(-b\right)+4a^{2}+b\left(-b\right)+2ba, find the opposite of each term.

$$4a^{2}-8ab+4b^{2}-2a\left(-b\right)-4a^{2}-b\left(-b\right)-2ba$$

Multiply -2 and -1 to get 2.

$$4a^{2}-8ab+4b^{2}+2ab-4a^{2}-b\left(-b\right)-2ba$$

Combine -8ab and 2ab to get -6ab.

$$4a^{2}-6ab+4b^{2}-4a^{2}-b\left(-b\right)-2ba$$

Combine 4a^{2} and -4a^{2} to get 0.

$$-6ab+4b^{2}-b\left(-b\right)-2ba$$

Multiply -1 and -1 to get 1.

$$-6ab+4b^{2}+bb-2ba$$

Multiply b and b to get b^{2}.

$$-6ab+4b^{2}+b^{2}-2ba$$

Combine 4b^{2} and b^{2} to get 5b^{2}.

$$-6ab+5b^{2}-2ba$$

Combine -6ab and -2ba to get -8ab.

$$-8ab+5b^{2}$$

Expand

$$5b^{2}-8ab$$

Solution Steps

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

$$4\left(a^{2}-2ab+b^{2}\right)-\left(2a+b\right)\left(-b+2a\right)$$

Use the distributive property to multiply 4 by a^{2}-2ab+b^{2}.

$$4a^{2}-8ab+4b^{2}-\left(2a+b\right)\left(-b+2a\right)$$

Use the distributive property to multiply 2a+b by -b+2a.

$$4a^{2}-8ab+4b^{2}-\left(2a\left(-b\right)+4a^{2}+b\left(-b\right)+2ba\right)$$

To find the opposite of 2a\left(-b\right)+4a^{2}+b\left(-b\right)+2ba, find the opposite of each term.

$$4a^{2}-8ab+4b^{2}-2a\left(-b\right)-4a^{2}-b\left(-b\right)-2ba$$

Multiply -2 and -1 to get 2.

$$4a^{2}-8ab+4b^{2}+2ab-4a^{2}-b\left(-b\right)-2ba$$

Combine -8ab and 2ab to get -6ab.

$$4a^{2}-6ab+4b^{2}-4a^{2}-b\left(-b\right)-2ba$$

Combine 4a^{2} and -4a^{2} to get 0.

$$-6ab+4b^{2}-b\left(-b\right)-2ba$$

Multiply -1 and -1 to get 1.

$$-6ab+4b^{2}+bb-2ba$$

Multiply b and b to get b^{2}.

$$-6ab+4b^{2}+b^{2}-2ba$$

Combine 4b^{2} and b^{2} to get 5b^{2}.

$$-6ab+5b^{2}-2ba$$

Combine -6ab and -2ba to get -8ab.

$$-8ab+5b^{2}$$