Questions: (3x^2-2x)(3x^2+2x)= □ (Simplify your answer.)

Transcript text: \[ \left(3 x^{2}-2 x\right)\left(3 x^{2}+2 x\right) \] $\left(3 x^{2}-2 x\right)\left(3 x^{2}+2 x\right)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

To find the product of $(3x^2 - 2x)(3x^2 + 2x)$, we can use the difference of squares formula, which states that $(a - b)(a + b) = a^2 - b^2$. Here, $a = 3x^2$ and $b = 2x$.

Solution Approach

Identify $a$ and $b$ in the given expression.
Apply the difference of squares formula: $(a - b)(a + b) = a^2 - b^2$.
Simplify the resulting expression.

Step 1: Understand the Problem

We need to find the product of two binomials: \[ (3x^2 - 2x)(3x^2 + 2x) \]

Step 2: Apply the Difference of Squares Formula

Notice that the expression is in the form of $(a - b)(a + b)$, which can be simplified using the difference of squares formula: \[ (a - b)(a + b) = a^2 - b^2 \] Here, $a = 3x^2$ and $b = 2x$.

Step 3: Calculate $a^2$

\[ a^2 = (3x^2)^2 = 9x^4 \]

Step 4: Calculate $b^2$

\[ b^2 = (2x)^2 = 4x^2 \]

Step 5: Apply the Difference of Squares Formula

\[ (3x^2 - 2x)(3x^2 + 2x) = a^2 - b^2 = 9x^4 - 4x^2 \]