Solve (x+2)(x+3)(x+4)(x+5)-24 | 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

$$(x+2)(x+3)(x+4)(x+5)-24$$

Evaluate

$\left(x+1\right)\left(x+6\right)\left(x^{2}+7x+16\right)$

Solution Steps

Apply the distributive property by multiplying each term of $x+2$ by each term of $x+3$.

$$\left(x^{2}+3x+2x+6\right)\left(x+4\right)\left(x+5\right)-24$$

Combine $3x$ and $2x$ to get $5x$.

$$\left(x^{2}+5x+6\right)\left(x+4\right)\left(x+5\right)-24$$

Apply the distributive property by multiplying each term of $x^{2}+5x+6$ by each term of $x+4$.

$$\left(x^{3}+4x^{2}+5x^{2}+20x+6x+24\right)\left(x+5\right)-24$$

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

$$\left(x^{3}+9x^{2}+20x+6x+24\right)\left(x+5\right)-24$$

Combine $20x$ and $6x$ to get $26x$.

$$\left(x^{3}+9x^{2}+26x+24\right)\left(x+5\right)-24$$

Apply the distributive property by multiplying each term of $x^{3}+9x^{2}+26x+24$ by each term of $x+5$.

$$x^{4}+5x^{3}+9x^{3}+45x^{2}+26x^{2}+130x+24x+120-24$$

Combine $5x^{3}$ and $9x^{3}$ to get $14x^{3}$.

$$x^{4}+14x^{3}+45x^{2}+26x^{2}+130x+24x+120-24$$

Combine $45x^{2}$ and $26x^{2}$ to get $71x^{2}$.

$$x^{4}+14x^{3}+71x^{2}+130x+24x+120-24$$

Combine $130x$ and $24x$ to get $154x$.

$$x^{4}+14x^{3}+71x^{2}+154x+120-24$$

Subtract $24$ from $120$ to get $96$.

$$x^{4}+14x^{3}+71x^{2}+154x+96$$

Expand

$x^{4}+14x^{3}+71x^{2}+154x+96$

Solution Steps

Apply the distributive property by multiplying each term of $x+2$ by each term of $x+3$.

$$\left(x^{2}+3x+2x+6\right)\left(x+4\right)\left(x+5\right)-24$$

Combine $3x$ and $2x$ to get $5x$.

$$\left(x^{2}+5x+6\right)\left(x+4\right)\left(x+5\right)-24$$

Apply the distributive property by multiplying each term of $x^{2}+5x+6$ by each term of $x+4$.

$$\left(x^{3}+4x^{2}+5x^{2}+20x+6x+24\right)\left(x+5\right)-24$$

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

$$\left(x^{3}+9x^{2}+20x+6x+24\right)\left(x+5\right)-24$$

Combine $20x$ and $6x$ to get $26x$.

$$\left(x^{3}+9x^{2}+26x+24\right)\left(x+5\right)-24$$

Apply the distributive property by multiplying each term of $x^{3}+9x^{2}+26x+24$ by each term of $x+5$.

$$x^{4}+5x^{3}+9x^{3}+45x^{2}+26x^{2}+130x+24x+120-24$$

Combine $5x^{3}$ and $9x^{3}$ to get $14x^{3}$.

$$x^{4}+14x^{3}+45x^{2}+26x^{2}+130x+24x+120-24$$

Combine $45x^{2}$ and $26x^{2}$ to get $71x^{2}$.

$$x^{4}+14x^{3}+71x^{2}+130x+24x+120-24$$

Combine $130x$ and $24x$ to get $154x$.

$$x^{4}+14x^{3}+71x^{2}+154x+120-24$$

Subtract $24$ from $120$ to get $96$.

$$x^{4}+14x^{3}+71x^{2}+154x+96$$