Solve 4 ) (c - 3d) ^ 2 - (c + 3d) ^ 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

$$( c - 3 d ) ^ { 2 } - ( c + 3 d ) ^ { 2 }$$

Evaluate

$-12cd$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(c-3d\right)^{2}$.

$$c^{2}-6cd+9d^{2}-\left(c+3d\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(c+3d\right)^{2}$.

$$c^{2}-6cd+9d^{2}-\left(c^{2}+6cd+9d^{2}\right)$$

To find the opposite of $c^{2}+6cd+9d^{2}$, find the opposite of each term.

$$c^{2}-6cd+9d^{2}-c^{2}-6cd-9d^{2}$$

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

$$-6cd+9d^{2}-6cd-9d^{2}$$

Combine $-6cd$ and $-6cd$ to get $-12cd$.

$$-12cd+9d^{2}-9d^{2}$$

Combine $9d^{2}$ and $-9d^{2}$ to get $0$.

$$-12cd$$

Expand

$-12cd$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(c-3d\right)^{2}$.

$$c^{2}-6cd+9d^{2}-\left(c+3d\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(c+3d\right)^{2}$.

$$c^{2}-6cd+9d^{2}-\left(c^{2}+6cd+9d^{2}\right)$$

To find the opposite of $c^{2}+6cd+9d^{2}$, find the opposite of each term.

$$c^{2}-6cd+9d^{2}-c^{2}-6cd-9d^{2}$$

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

$$-6cd+9d^{2}-6cd-9d^{2}$$

Combine $-6cd$ and $-6cd$ to get $-12cd$.

$$-12cd+9d^{2}-9d^{2}$$

Combine $9d^{2}$ and $-9d^{2}$ to get $0$.

$$-12cd$$