Problem 36 - College Algebra Essentials

Question

Find each product. $$(4-3 x)(4+3 x)$$

Step-by-Step Solution

Answer

The product of the two binomials \((4-3 x)\) and \((4+3 x)\) is \(16 - 9x^2\).

Step 1: Multiply the first terms

Multiply the first terms of each binomial i.e. multiply \(4\) from first binomial and \(4\) from the second binomial. Result of this multiplication is \(4*4 = 16\).

Step 2: Multiply the outer terms

Multiply the term from the outer of each binomial, i.e. multiply \(4\) from first binomial and \(3x\) from the second binomial. Result of this multiplication is \(4*3x = 12x\).

Step 3: Multiply the inner terms

Multiply the term from the inner of each binomial, i.e. multiply \(-3x\) from first binomial and \(4\) from the second binomial. Result of this multiplication is \(-3x*4=-12x\).

Step 4: Multiply the last terms

Multiply the last terms of each binomial i.e. multiply \(-3x\) from first binomial and \(3x\) from the second binomial. Result of this multiplication is \( -3x*3x = -9x^2\).

Step 5: Combine the terms

Now, combine all the calculated products, i.e. \(16+12x-12x-9x^2\). After combining, it can be seen that \(12x\) and \(-12x\) will cancel out each other.