Solve (3x-1)^(2)-(3x-2)(3x+1) | 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

$${ \left(3x-1 \right) }^{ 2 } -(3x-2)(3x+1)$$

Evaluate

$3-3x$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(3x-1\right)^{2}$.

$$9x^{2}-6x+1-\left(3x-2\right)\left(3x+1\right)$$

Use the distributive property to multiply $3x-2$ by $3x+1$ and combine like terms.

$$9x^{2}-6x+1-\left(9x^{2}-3x-2\right)$$

To find the opposite of $9x^{2}-3x-2$, find the opposite of each term.

$$9x^{2}-6x+1-9x^{2}+3x+2$$

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

$$-6x+1+3x+2$$

Combine $-6x$ and $3x$ to get $-3x$.

$$-3x+1+2$$

Add $1$ and $2$ to get $3$.

$$-3x+3$$

Expand

$3-3x$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(3x-1\right)^{2}$.

$$9x^{2}-6x+1-\left(3x-2\right)\left(3x+1\right)$$

Use the distributive property to multiply $3x-2$ by $3x+1$ and combine like terms.

$$9x^{2}-6x+1-\left(9x^{2}-3x-2\right)$$

To find the opposite of $9x^{2}-3x-2$, find the opposite of each term.

$$9x^{2}-6x+1-9x^{2}+3x+2$$

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

$$-6x+1+3x+2$$

Combine $-6x$ and $3x$ to get $-3x$.

$$-3x+1+2$$

Add $1$ and $2$ to get $3$.

$$-3x+3$$