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Chapter 0: Problem 38

Find each product. $$\left(3 x^{2}+4 x\right)\left(3 x^{2}-4 x\right)$$

Short Answer

Expert verified
The product is \(9x^{4} - 16x^{2}\)

Step by step solution

01

Expand the multiplication

We need to multiply every term in the first binomial by every term in the second binomial. This means that the first term \(3x^{2}\) is multiplied by every term in the second bracket and the same happens for the second term \(4x\). This results in four separate products.
02

Apply the distributive property

So, let's write down those separate products: \( (3x^{2} \cdot 3x^{2}) - (3x^{2} \cdot 4x) + (4x \cdot 3x^{2}) - (4x \cdot 4x) \)
03

Simplify each product

Now, for each product, we multiply the coefficients (the numbers) and add the exponents for \(x\) according to the law of exponents: \( 9x^{4} - 12x^{3} + 12x^{3} - 16x^{2} \)
04

Combine like terms

-12x^{3} + 12x^{3} = 0x^{3} which simplifies to 0. So, the final simplified expression is: \( 9x^{4} - 16x^{2} \)

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