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

Question

Simplify the expression

81 x^{4} - 72 x^{2} + 16

Evaluate

(9 x^{2} - 4) (9 x^{2} - 4)

Multiply the terms

(9 x^{2} - 4)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(9 x^{2})^{2} - 2 \times 9 x^{2} \times 4 + 4^{2}

Solution

81 x^{4} - 72 x^{2} + 16

Show Solution

(3 x - 2)^{2} (3 x + 2)^{2}

Evaluate

(9 x^{2} - 4) (9 x^{2} - 4)

Multiply the terms

(9 x^{2} - 4)^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

((3 x - 2) (3 x + 2))^{2}

Solution

(3 x - 2)^{2} (3 x + 2)^{2}

Show Solution

x_{1} = - \frac{2}{3}, x_{2} = \frac{2}{3}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0. \dot{6}

Evaluate

(9 x^{2} - 4) (9 x^{2} - 4)

To find the roots of the expression,set the expression equal to 0

(9 x^{2} - 4) (9 x^{2} - 4) = 0

Multiply the terms

(9 x^{2} - 4)^{2} = 0

The only way a power can be 0 is when the base equals 0

9 x^{2} - 4 = 0

Move the constant to the right-hand side and change its sign

9 x^{2} = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

9 x^{2} = 4

Divide both sides

\frac{9 x ^{2}}{9} = \frac{4}{9}

Divide the numbers

x^{2} = \frac{4}{9}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{4}{9}

Simplify the expression

More Steps

Evaluate

\frac{4}{9}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4}{9}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{2}{3}

x = \pm \frac{2}{3}

Separate the equation into 2 possible cases

x = \frac{2}{3} x = - \frac{2}{3}

Solution

x_{1} = - \frac{2}{3}, x_{2} = \frac{2}{3}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0. \dot{6}

Show Solution