Solve (a - b) ^ 2 - (a + b) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

$-4ab$

Solution Steps

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

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

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

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

To find the opposite of $a^{2}+2ab+b^{2}$, find the opposite of each term.

$$a^{2}-2ab+b^{2}-a^{2}-2ab-b^{2}$$

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

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

Combine $-2ab$ and $-2ab$ to get $-4ab$.

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

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

$$-4ab$$

Expand

$-4ab$

Solution Steps

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

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

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

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

To find the opposite of $a^{2}+2ab+b^{2}$, find the opposite of each term.

$$a^{2}-2ab+b^{2}-a^{2}-2ab-b^{2}$$

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

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

Combine $-2ab$ and $-2ab$ to get $-4ab$.

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

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

$$-4ab$$