Question

1. (9x + 2)(x + 6)
2. (4x + 5)^2

Explanation:

Problem 2: \((9x + 2)(x + 6)\)

Step 1: Apply the distributive property (FOIL method)

Multiply the First terms: \(9x \times x = 9x^2\)
Multiply the Outer terms: \(9x \times 6 = 54x\)
Multiply the Inner terms: \(2 \times x = 2x\)
Multiply the Last terms: \(2 \times 6 = 12\)

Step 2: Combine like terms

Combine the \(x\)-terms: \(54x + 2x = 56x\)
So, the expanded form is \(9x^2 + 56x + 12\)

Step 1: Use the formula \((a + b)^2 = a^2 + 2ab + b^2\)

Here, \(a = 4x\) and \(b = 5\)

Step 2: Substitute \(a\) and \(b\) into the formula

Calculate \(a^2\): \((4x)^2 = 16x^2\)
Calculate \(2ab\): \(2 \times 4x \times 5 = 40x\)
Calculate \(b^2\): \(5^2 = 25\)

Step 3: Combine the terms

The expanded form is \(16x^2 + 40x + 25\)

Answer:

\(9x^2 + 56x + 12\)

Problem 5: \((4x + 5)^2\)