Solve (4(x)^(2)-1)\times(4(x)^(2)-1)-(6(x)^(2)+x+1) | 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

$$(4 { x }^{ 2 } -1) \times (4 { x }^{ 2 } -1)-(6 { x }^{ 2 } +x+1)$$

Evaluate

$x\left(16x^{3}-14x-1\right)$

Solution Steps

Multiply $4x^{2}-1$ and $4x^{2}-1$ to get $\left(4x^{2}-1\right)^{2}$.

$$\left(4x^{2}-1\right)^{2}-\left(6x^{2}+x+1\right)$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x^{2}-1\right)^{2}$.

$$16\left(x^{2}\right)^{2}-8x^{2}+1-\left(6x^{2}+x+1\right)$$

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

$$16x^{4}-8x^{2}+1-\left(6x^{2}+x+1\right)$$

To find the opposite of $6x^{2}+x+1$, find the opposite of each term.

$$16x^{4}-8x^{2}+1-6x^{2}-x-1$$

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

$$16x^{4}-14x^{2}+1-x-1$$

Subtract $1$ from $1$ to get $0$.

$$16x^{4}-14x^{2}-x$$

Expand

$16x^{4}-14x^{2}-x$

Solution Steps

Multiply $4x^{2}-1$ and $4x^{2}-1$ to get $\left(4x^{2}-1\right)^{2}$.

$$\left(4x^{2}-1\right)^{2}-\left(6x^{2}+x+1\right)$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(4x^{2}-1\right)^{2}$.

$$16\left(x^{2}\right)^{2}-8x^{2}+1-\left(6x^{2}+x+1\right)$$

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

$$16x^{4}-8x^{2}+1-\left(6x^{2}+x+1\right)$$

To find the opposite of $6x^{2}+x+1$, find the opposite of each term.

$$16x^{4}-8x^{2}+1-6x^{2}-x-1$$

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

$$16x^{4}-14x^{2}+1-x-1$$

Subtract $1$ from $1$ to get $0$.

$$16x^{4}-14x^{2}-x$$