Problem 20 - College Algebra Essentials

Question

Find each product. $$(x+8)(x+5)$$

Step-by-Step Solution

Answer

The product of \((x+8)(x+5)\) is \(x^2 + 13x + 40\).

Step 1: First

Multiply the first terms in each bracket: \(x \times x = x^2\). The 'First' in the FOIL acronym means to multiply these terms together.

Step 2: Outer

Multiply the outer terms in the expression: \(x \times 5 = 5x\). The 'Outer' in the FOIL acronym means to multiply these terms together.

Step 3: Inner

Multiply the inner terms in the expression: \(8 \times x = 8x\). The 'Inner' in the FOIL acronym means to multiply these terms together.

Step 4: Last

Multiply the last terms in each bracket: \(8 \times 5 = 40\). The 'Last' in the FOIL acronym means to multiply these terms together.

Step 5: Sum up

Add up all the obtained results from the above steps: \(x^2 + 5x + 8x + 40\).

Step 6: Combine like terms

The terms \(5x\) and \(8x\) are like terms and can be combined to give \(13x\). Final answer is \(x^2 + 13x + 40\).