Question

Question:

Expand the expression below to find the values of the capitalised pronumerals.
(x + 3y)(2x - 3y) = Ax2 + Bxy + Cy2
A=
B=
C=

Answer 1

The value of A is equal to 2.

The value of B is equal to 3.

The value of C is equal to -9.

General Formulas and Concepts:
Pre-Algebra

• Distributive Property

Algebra I

Terms/Coefficients

• Expanding/Factoring (FOIL Method)

Explanation:

Step 1: Define

Identify given.

(x + 3y)(2x - 3y)

Step 2: Rewrite

Use FOIL: First, Outside, Inside, Last.

1. [Expression] Expand [FOIL]:
   (x + 3y)(2x - 3y) = 2x² - 3xy + 6xy - 9y²
2. [Expression] Combine like terms (xy):
   (x + 3y)(2x - 3y) = 2x² + 3xy - 9y²
3. [Expression] Identify leading coefficients:
   A = 2, B = 3, C = -9

∴ we are done!

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Topic: Algebra I