Solve (2a - 5b) ^ 2 - (5a - 2b) ^ 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

$$(2a-5b)^{2}-(5a-2b)^{2}$$

Evaluate

$21\left(b^{2}-a^{2}\right)$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(2a-5b\right)^{2}$.

$$4a^{2}-20ab+25b^{2}-\left(5a-2b\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(5a-2b\right)^{2}$.

$$4a^{2}-20ab+25b^{2}-\left(25a^{2}-20ab+4b^{2}\right)$$

To find the opposite of $25a^{2}-20ab+4b^{2}$, find the opposite of each term.

$$4a^{2}-20ab+25b^{2}-25a^{2}+20ab-4b^{2}$$

Combine $4a^{2}$ and $-25a^{2}$ to get $-21a^{2}$.

$$-21a^{2}-20ab+25b^{2}+20ab-4b^{2}$$

Combine $-20ab$ and $20ab$ to get $0$.

$$-21a^{2}+25b^{2}-4b^{2}$$

Combine $25b^{2}$ and $-4b^{2}$ to get $21b^{2}$.

$$-21a^{2}+21b^{2}$$

Expand

$21b^{2}-21a^{2}$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(2a-5b\right)^{2}$.

$$4a^{2}-20ab+25b^{2}-\left(5a-2b\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(5a-2b\right)^{2}$.

$$4a^{2}-20ab+25b^{2}-\left(25a^{2}-20ab+4b^{2}\right)$$

To find the opposite of $25a^{2}-20ab+4b^{2}$, find the opposite of each term.

$$4a^{2}-20ab+25b^{2}-25a^{2}+20ab-4b^{2}$$

Combine $4a^{2}$ and $-25a^{2}$ to get $-21a^{2}$.

$$-21a^{2}-20ab+25b^{2}+20ab-4b^{2}$$

Combine $-20ab$ and $20ab$ to get $0$.

$$-21a^{2}+25b^{2}-4b^{2}$$

Combine $25b^{2}$ and $-4b^{2}$ to get $21b^{2}$.

$$-21a^{2}+21b^{2}$$