Question

1. (4x - 3)(3x + 11)
2. (7x - 3)^2

Explanation:

Problem 3: \((4x - 3)(3x + 11)\)

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(4x \cdot 3x = 12x^2\)
Multiply the Outer terms: \(4x \cdot 11 = 44x\)
Multiply the Inner terms: \(-3 \cdot 3x = -9x\)
Multiply the Last terms: \(-3 \cdot 11 = -33\)

Step2: Combine like terms

Combine the \(x\)-terms: \(44x - 9x = 35x\)

So, \((4x - 3)(3x + 11) = 12x^2 + 35x - 33\)

Problem 6: \((7x - 3)^2\)

Step1: Recognize the perfect square formula \((a - b)^2 = a^2 - 2ab + b^2\)

Here, \(a = 7x\) and \(b = 3\)

Step2: Substitute into the formula

Calculate \(a^2\): \((7x)^2 = 49x^2\)
Calculate \(-2ab\): \(-2 \cdot 7x \cdot 3 = -42x\)
Calculate \(b^2\): \(3^2 = 9\)

Step3: Combine the terms

\((7x - 3)^2 = 49x^2 - 42x + 9\)

Answer:

s:

1. \(\boldsymbol{12x^2 + 35x - 33}\)
2. \(\boldsymbol{49x^2 - 42x + 9}\)