Question

multiply each of the following binom

1. (3x - 4)(7x - 5)

1. (3x - 10)(3x + 10)

Explanation:

Problem 1: \((3x - 4)(7x - 5)\)

Step 1: Apply the distributive property (FOIL method)

Multiply the First terms: \(3x \times 7x = 21x^2\)
Multiply the Outer terms: \(3x \times (-5) = -15x\)
Multiply the Inner terms: \(-4 \times 7x = -28x\)
Multiply the Last terms: \(-4 \times (-5) = 20\)

Step 2: Combine like terms

Combine the middle terms (\(-15x\) and \(-28x\)):
\(-15x - 28x = -43x\)

Step 3: Write the final expression

Combine all terms: \(21x^2 - 43x + 20\)

Step 1: Recognize the difference of squares formula

The expression is in the form \((a - b)(a + b) = a^2 - b^2\), where \(a = 3x\) and \(b = 10\).

Step 2: Apply the difference of squares formula

Substitute \(a = 3x\) and \(b = 10\) into the formula:
\((3x)^2 - (10)^2\)

Step 3: Simplify the terms

Calculate \((3x)^2 = 9x^2\) and \((10)^2 = 100\):
\(9x^2 - 100\)

Answer:

\(21x^2 - 43x + 20\)

Problem 4: \((3x - 10)(3x + 10)\)