How do I factor this expression? 4a^2 – 4ab + b^2 + 16a – 8b + 15

Question

Math Experts! How do I factor this expression?

4a^2 – 4ab + b^2 + 16a – 8b + 15 Please tell me how you answered it, thank you!

Answer 1

The expression is 4a² - 4ab + b² +16a - 8b +15.

Group like terms.

= (4a² - 4ab + b²) +(16a - 8b +15)

= [(2a)² - 2(2a)(b) + (b)²] +(16a - 8b +15)

Apply suare of a difference formula : (a - b)² = a² - 2ab +b².

(2a - b)² +(16a - 8b +15)

The factorization fom of (4a² - 4ab + b² +16a - 8b +15) is (2a - b)² +(16a - 8b +15).