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

$$( - a + b ) ^ { 2 } - ( 2 a - b ) \cdot ( - b - 2 a )$$

Evaluate

$$a\left(5a-2b\right)$$

Solution Steps

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

Multiply -1 and -1 to get 1.

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

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

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

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

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

Multiply -2 and -1 to get 2.

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

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

$$5a^{2}+2\left(-a\right)b+b^{2}+2ab-b^{2}-2ba$$

Combine b^{2} and -b^{2} to get 0.

$$5a^{2}+2\left(-a\right)b+2ab-2ba$$

Combine 2ab and -2ba to get 0.

$$5a^{2}+2\left(-a\right)b$$

Multiply 2 and -1 to get -2.

$$5a^{2}-2ab$$

Expand

$$5a^{2}-2ab$$

Solution Steps

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

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

Calculate -a to the power of 2 and get a^{2}.

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

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

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

Multiply -1 and -1 to get 1.

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

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

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

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

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

Multiply -2 and -1 to get 2.

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

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

$$5a^{2}+2\left(-a\right)b+b^{2}+2ab-b^{2}-2ba$$

Combine b^{2} and -b^{2} to get 0.

$$5a^{2}+2\left(-a\right)b+2ab-2ba$$

Combine 2ab and -2ba to get 0.

$$5a^{2}+2\left(-a\right)b$$

Multiply 2 and -1 to get -2.

$$5a^{2}-2ab$$