Solve (x-(3)/(4))(x+(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

$$(x- \frac{ 3 }{ 4 } )(x+ \frac{ 3 }{ 2 } )$$

Evaluate

$x^{2}+\frac{3x}{4}-\frac{9}{8}$

Solution Steps

Apply the distributive property by multiplying each term of $x-\frac{3}{4}$ by each term of $x+\frac{3}{2}$.

$$x^{2}+x\times \frac{3}{2}-\frac{3}{4}x-\frac{3}{4}\times \frac{3}{2}$$

Combine $x\times \frac{3}{2}$ and $-\frac{3}{4}x$ to get $\frac{3}{4}x$.

$$x^{2}+\frac{3}{4}x-\frac{3}{4}\times \frac{3}{2}$$

Multiply $-\frac{3}{4}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{3}{4}x+\frac{-3\times 3}{4\times 2}$$

Do the multiplications in the fraction $\frac{-3\times 3}{4\times 2}$.

$$x^{2}+\frac{3}{4}x+\frac{-9}{8}$$

Fraction $\frac{-9}{8}$ can be rewritten as $-\frac{9}{8}$ by extracting the negative sign.

$$x^{2}+\frac{3}{4}x-\frac{9}{8}$$

Expand

$x^{2}+\frac{3x}{4}-\frac{9}{8}$

Solution Steps

Apply the distributive property by multiplying each term of $x-\frac{3}{4}$ by each term of $x+\frac{3}{2}$.

$$x^{2}+x\times \frac{3}{2}-\frac{3}{4}x-\frac{3}{4}\times \frac{3}{2}$$

Combine $x\times \frac{3}{2}$ and $-\frac{3}{4}x$ to get $\frac{3}{4}x$.

$$x^{2}+\frac{3}{4}x-\frac{3}{4}\times \frac{3}{2}$$

Multiply $-\frac{3}{4}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{3}{4}x+\frac{-3\times 3}{4\times 2}$$

Do the multiplications in the fraction $\frac{-3\times 3}{4\times 2}$.

$$x^{2}+\frac{3}{4}x+\frac{-9}{8}$$

Fraction $\frac{-9}{8}$ can be rewritten as $-\frac{9}{8}$ by extracting the negative sign.

$$x^{2}+\frac{3}{4}x-\frac{9}{8}$$