Solve 36 * (a - b) ^ 2 - 25 * (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

$$36(a-b)^{2}-25(a+b)^{2}$$

Evaluate

$\left(a-11b\right)\left(11a-b\right)$

Solution Steps

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

$$36\left(a^{2}-2ab+b^{2}\right)-25\left(a+b\right)^{2}$$

Use the distributive property to multiply $36$ by $a^{2}-2ab+b^{2}$.

$$36a^{2}-72ab+36b^{2}-25\left(a+b\right)^{2}$$

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

$$36a^{2}-72ab+36b^{2}-25\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply $-25$ by $a^{2}+2ab+b^{2}$.

$$36a^{2}-72ab+36b^{2}-25a^{2}-50ab-25b^{2}$$

Combine $36a^{2}$ and $-25a^{2}$ to get $11a^{2}$.

$$11a^{2}-72ab+36b^{2}-50ab-25b^{2}$$

Combine $-72ab$ and $-50ab$ to get $-122ab$.

$$11a^{2}-122ab+36b^{2}-25b^{2}$$

Combine $36b^{2}$ and $-25b^{2}$ to get $11b^{2}$.

$$11a^{2}-122ab+11b^{2}$$

Expand

$11a^{2}-122ab+11b^{2}$

Solution Steps

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

$$36\left(a^{2}-2ab+b^{2}\right)-25\left(a+b\right)^{2}$$

Use the distributive property to multiply $36$ by $a^{2}-2ab+b^{2}$.

$$36a^{2}-72ab+36b^{2}-25\left(a+b\right)^{2}$$

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

$$36a^{2}-72ab+36b^{2}-25\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply $-25$ by $a^{2}+2ab+b^{2}$.

$$36a^{2}-72ab+36b^{2}-25a^{2}-50ab-25b^{2}$$

Combine $36a^{2}$ and $-25a^{2}$ to get $11a^{2}$.

$$11a^{2}-72ab+36b^{2}-50ab-25b^{2}$$

Combine $-72ab$ and $-50ab$ to get $-122ab$.

$$11a^{2}-122ab+36b^{2}-25b^{2}$$

Combine $36b^{2}$ and $-25b^{2}$ to get $11b^{2}$.

$$11a^{2}-122ab+11b^{2}$$