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(ii) 4x^(2)-y^(2)-3xy+2x-2y

2 min read Jun 16, 2024
(ii) 4x^(2)-y^(2)-3xy+2x-2y

Factoring the Expression: 4x^(2)-y^(2)-3xy+2x-2y

This expression represents a quadratic equation with two variables, x and y. Factoring this expression involves breaking it down into simpler expressions that can be multiplied together to get the original expression. Here's how we can approach it:

Grouping and Factoring

  1. Group Similar Terms: Group the terms with similar variables together: (4x^(2) - 3xy + 2x) + (-y^(2) - 2y)

  2. Factor Out Common Factors:

    • From the first group: x(4x - 3y + 2)
    • From the second group: -y(y + 2)

  3. Combine Factored Expressions: This gives us the factored form: x(4x - 3y + 2) - y(y + 2)

Simplifying (Optional)

While the expression is already factored, we can try to simplify it further by looking for patterns or common factors. However, in this case, there isn't a straightforward simplification that can be done.

Conclusion

The factored form of the expression 4x^(2)-y^(2)-3xy+2x-2y is x(4x - 3y + 2) - y(y + 2).

Important Note: Factoring expressions helps us analyze and solve equations involving multiple variables. It's a fundamental skill in algebra and can be applied to various mathematical problems.

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