Which of the following represents the correct factorization of $ x^2 + (a-b)x - ab $?

Question

Examoogle · Accepted Answer

The correct answer is Option D: $x^2 + (a+b)x + ab$. Use the FOIL method (First, Outer, Inner, Last): $x \cdot x + x \cdot b + a \cdot x + a \cdot b = x^2 + (a+b)x + ab$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the FOIL method (First, Outer, Inner, Last): $x \cdot x + x \cdot b + a \cdot x + a \cdot b = x^2 + (a+b)x + ab$.

Formula Used: $$(x + a)(x + b) = x^2 + (a + b)x + ab$$

Given: Two binomial terms $(x + a)$ and $(x + b)$

Steps: Step 1: Understand the expression: We need to find the product of two binomial expressions: $(x + a)$ and $(x + b)$.. Step 2: Apply the distributive property (FOIL): Multiply each term in the first binomial by each term in the second binomial: First ($x \cdot x$), Outer ($x \cdot b$), Inner ($a \cdot x$), Last ($a \cdot b$).. Step 3: Simplify and combine like terms: Combine the terms containing $x$, which gives $(a + b)x$, and keep the constant product $ab$.

Answer: D is correct because expanding the product using the distributive property gives x² + (a + b)x + ab.

Exam Tip: Recognizing standard algebraic identities saves significant time in quadratic factorization and polynomial equations.

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