Solve (3x-2)^(2)-(2x+3)^(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

$${ \left(3x-2 \right) }^{ 2 } - { \left(2x+3 \right) }^{ 2 }$$

Evaluate

$\left(x-5\right)\left(5x+1\right)$

Solution Steps

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

$$9x^{2}-12x+4-\left(2x+3\right)^{2}$$

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

$$9x^{2}-12x+4-\left(4x^{2}+12x+9\right)$$

To find the opposite of $4x^{2}+12x+9$, find the opposite of each term.

$$9x^{2}-12x+4-4x^{2}-12x-9$$

Combine $9x^{2}$ and $-4x^{2}$ to get $5x^{2}$.

$$5x^{2}-12x+4-12x-9$$

Combine $-12x$ and $-12x$ to get $-24x$.

$$5x^{2}-24x+4-9$$

Subtract $9$ from $4$ to get $-5$.

$$5x^{2}-24x-5$$

Expand

$5x^{2}-24x-5$

Solution Steps

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

$$9x^{2}-12x+4-\left(2x+3\right)^{2}$$

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

$$9x^{2}-12x+4-\left(4x^{2}+12x+9\right)$$

To find the opposite of $4x^{2}+12x+9$, find the opposite of each term.

$$9x^{2}-12x+4-4x^{2}-12x-9$$

Combine $9x^{2}$ and $-4x^{2}$ to get $5x^{2}$.

$$5x^{2}-12x+4-12x-9$$

Combine $-12x$ and $-12x$ to get $-24x$.

$$5x^{2}-24x+4-9$$

Subtract $9$ from $4$ to get $-5$.

$$5x^{2}-24x-5$$