Question

multiply.
(4x + 3z)(7x + 5z)
simplify your answer.

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
\((4x)(7x) + (4x)(5z) + (3z)(7x) + (3z)(5z)\)

Step2: Calculate each product

• \((4x)(7x) = 28x^2\)
• \((4x)(5z) = 20xz\)
• \((3z)(7x) = 21xz\)
• \((3z)(5z) = 15z^2\)

Step3: Combine like terms

Add the \(xz\) terms: \(20xz + 21xz = 41xz\)

Step4: Write the simplified expression

Combine all terms: \(28x^2 + 41xz + 15z^2\)

Answer:

\(28x^2 + 41xz + 15z^2\)