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

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

Evaluate

$-8cd$

Solution Steps

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

$$4c^{2}-4cd+d^{2}-\left(2c+d\right)^{2}$$

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

$$4c^{2}-4cd+d^{2}-\left(4c^{2}+4cd+d^{2}\right)$$

To find the opposite of $4c^{2}+4cd+d^{2}$, find the opposite of each term.

$$4c^{2}-4cd+d^{2}-4c^{2}-4cd-d^{2}$$

Combine $4c^{2}$ and $-4c^{2}$ to get $0$.

$$-4cd+d^{2}-4cd-d^{2}$$

Combine $-4cd$ and $-4cd$ to get $-8cd$.

$$-8cd+d^{2}-d^{2}$$

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

$$-8cd$$

Expand

$-8cd$

Solution Steps

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

$$4c^{2}-4cd+d^{2}-\left(2c+d\right)^{2}$$

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

$$4c^{2}-4cd+d^{2}-\left(4c^{2}+4cd+d^{2}\right)$$

To find the opposite of $4c^{2}+4cd+d^{2}$, find the opposite of each term.

$$4c^{2}-4cd+d^{2}-4c^{2}-4cd-d^{2}$$

Combine $4c^{2}$ and $-4c^{2}$ to get $0$.

$$-4cd+d^{2}-4cd-d^{2}$$

Combine $-4cd$ and $-4cd$ to get $-8cd$.

$$-8cd+d^{2}-d^{2}$$

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

$$-8cd$$