Solve 4((x)^(2)-3)^(2)-5((x)^(2)-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

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

Evaluate

$4x^{4}-29x^{2}+53$

Solution Steps

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

$$4\left(\left(x^{2}\right)^{2}-6x^{2}+9\right)-5\left(x^{2}-3\right)+2$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$4\left(x^{4}-6x^{2}+9\right)-5\left(x^{2}-3\right)+2$$

Use the distributive property to multiply $4$ by $x^{4}-6x^{2}+9$.

$$4x^{4}-24x^{2}+36-5\left(x^{2}-3\right)+2$$

Use the distributive property to multiply $-5$ by $x^{2}-3$.

$$4x^{4}-24x^{2}+36-5x^{2}+15+2$$

Combine $-24x^{2}$ and $-5x^{2}$ to get $-29x^{2}$.

$$4x^{4}-29x^{2}+36+15+2$$

Add $36$ and $15$ to get $51$.

$$4x^{4}-29x^{2}+51+2$$

Add $51$ and $2$ to get $53$.

$$4x^{4}-29x^{2}+53$$

Expand

$4x^{4}-29x^{2}+53$

Solution Steps

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

$$4\left(\left(x^{2}\right)^{2}-6x^{2}+9\right)-5\left(x^{2}-3\right)+2$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$4\left(x^{4}-6x^{2}+9\right)-5\left(x^{2}-3\right)+2$$

Use the distributive property to multiply $4$ by $x^{4}-6x^{2}+9$.

$$4x^{4}-24x^{2}+36-5\left(x^{2}-3\right)+2$$

Use the distributive property to multiply $-5$ by $x^{2}-3$.

$$4x^{4}-24x^{2}+36-5x^{2}+15+2$$

Combine $-24x^{2}$ and $-5x^{2}$ to get $-29x^{2}$.

$$4x^{4}-29x^{2}+36+15+2$$

Add $36$ and $15$ to get $51$.

$$4x^{4}-29x^{2}+51+2$$

Add $51$ and $2$ to get $53$.

$$4x^{4}-29x^{2}+53$$