Question

1. (x+3)(x+4) (3+x)(4+x) (x−3)(x−4)

Explanation:

Assuming the task is to expand these binomial products, we'll do each one:

For \((x + 3)(x + 4)\)

Step1: Use FOIL method (First, Outer, Inner, Last)

First: \(x \times x = x^2\)
Outer: \(x \times 4 = 4x\)
Inner: \(3 \times x = 3x\)
Last: \(3 \times 4 = 12\)

Step2: Combine like terms

\(x^2 + 4x + 3x + 12 = x^2 + 7x + 12\)

For \((3 + x)(4 + x)\)

Step1: Use FOIL method

First: \(3 \times 4 = 12\)
Outer: \(3 \times x = 3x\)
Inner: \(x \times 4 = 4x\)
Last: \(x \times x = x^2\)

Step2: Combine like terms

\(12 + 3x + 4x + x^2 = x^2 + 7x + 12\)

For \((x - 3)(x - 4)\)

Step1: Use FOIL method

First: \(x \times x = x^2\)
Outer: \(x \times (-4) = -4x\)
Inner: \((-3) \times x = -3x\)
Last: \((-3) \times (-4) = 12\)

Step2: Combine like terms

\(x^2 - 4x - 3x + 12 = x^2 - 7x + 12\)

Answer:

s:

• \((x + 3)(x + 4) = \boldsymbol{x^2 + 7x + 12}\)
• \((3 + x)(4 + x) = \boldsymbol{x^2 + 7x + 12}\)
• \((x - 3)(x - 4) = \boldsymbol{x^2 - 7x + 12}\)