Solve Find the product of the expression (x - 2) and (x - 3) | 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

$$( x - 2 ) ( x - 3 ) ( x - 3 )$$

Evaluate

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

Solution Steps

Multiply $x-3$ and $x-3$ to get $\left(x-3\right)^{2}$.

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

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

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

Apply the distributive property by multiplying each term of $x-2$ by each term of $x^{2}-6x+9$.

$$x^{3}-6x^{2}+9x-2x^{2}+12x-18$$

Combine $-6x^{2}$ and $-2x^{2}$ to get $-8x^{2}$.

$$x^{3}-8x^{2}+9x+12x-18$$

Combine $9x$ and $12x$ to get $21x$.

$$x^{3}-8x^{2}+21x-18$$

Expand

$x^{3}-8x^{2}+21x-18$

Solution Steps

Multiply $x-3$ and $x-3$ to get $\left(x-3\right)^{2}$.

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

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

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

Apply the distributive property by multiplying each term of $x-2$ by each term of $x^{2}-6x+9$.

$$x^{3}-6x^{2}+9x-2x^{2}+12x-18$$

Combine $-6x^{2}$ and $-2x^{2}$ to get $-8x^{2}$.

$$x^{3}-8x^{2}+9x+12x-18$$

Combine $9x$ and $12x$ to get $21x$.

$$x^{3}-8x^{2}+21x-18$$