Solve (x ^ 2 + 4) ^ 2 + 6(x ^ 2 - 4) + 9 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

$$( x ^ { 2 } + 4 ) ^ { 2 } + 6 ( x ^ { 2 } - 4 ) + 9$$

Evaluate

$x^{4}+14x^{2}+1$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x^{2}+4\right)^{2}$.

$$\left(x^{2}\right)^{2}+8x^{2}+16+6\left(x^{2}-4\right)+9$$

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

$$x^{4}+8x^{2}+16+6\left(x^{2}-4\right)+9$$

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

$$x^{4}+8x^{2}+16+6x^{2}-24+9$$

Combine $8x^{2}$ and $6x^{2}$ to get $14x^{2}$.

$$x^{4}+14x^{2}+16-24+9$$

Subtract $24$ from $16$ to get $-8$.

$$x^{4}+14x^{2}-8+9$$

Add $-8$ and $9$ to get $1$.

$$x^{4}+14x^{2}+1$$

Expand

$x^{4}+14x^{2}+1$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x^{2}+4\right)^{2}$.

$$\left(x^{2}\right)^{2}+8x^{2}+16+6\left(x^{2}-4\right)+9$$

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

$$x^{4}+8x^{2}+16+6\left(x^{2}-4\right)+9$$

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

$$x^{4}+8x^{2}+16+6x^{2}-24+9$$

Combine $8x^{2}$ and $6x^{2}$ to get $14x^{2}$.

$$x^{4}+14x^{2}+16-24+9$$

Subtract $24$ from $16$ to get $-8$.

$$x^{4}+14x^{2}-8+9$$

Add $-8$ and $9$ to get $1$.

$$x^{4}+14x^{2}+1$$