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(8x-y)(x+3y)-(4x+y)(9y-2x)

2 min read Jun 16, 2024
(8x-y)(x+3y)-(4x+y)(9y-2x)

Simplifying Algebraic Expressions: (8x-y)(x+3y)-(4x+y)(9y-2x)

This article will guide you through the process of simplifying the algebraic expression: (8x-y)(x+3y)-(4x+y)(9y-2x)

Step 1: Expand the Expressions

We start by expanding the brackets using the distributive property (also known as FOIL - First, Outer, Inner, Last).

(8x-y)(x+3y) becomes:

  • 8x * x + 8x * 3y - y * x - y * 3y
  • 8x² + 24xy - xy - 3y²

(4x+y)(9y-2x) becomes:

  • 4x * 9y + 4x * -2x + y * 9y + y * -2x
  • 36xy - 8x² + 9y² - 2xy

Step 2: Combine Like Terms

Now we combine the like terms from both expanded expressions:

  • 8x² + 24xy - xy - 3y² - (36xy - 8x² + 9y² - 2xy)

  • 8x² + 24xy - xy - 3y² - 36xy + 8x² - 9y² + 2xy

Step 3: Simplify

Finally, we simplify by adding and subtracting the coefficients of the like terms:

  • (8x² + 8x²) + (24xy - xy - 36xy + 2xy) + (-3y² - 9y²)

  • 16x² - 11xy - 12y²

Therefore, the simplified form of the expression (8x-y)(x+3y)-(4x+y)(9y-2x) is 16x² - 11xy - 12y².

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