It looks like you have the expression: \[ x^{2} + 5xy - 36y \] To factor this expression, let's analyze it step by step. ### Step 1: Identify Common Factors First, check if there's a common factor in all the terms. In this case, the term $$ y $$ is a common factor in the last two terms. ### Step 2: Factor Out the Common Term Factor out $$ y $$ from the terms that include it: \[ x^{2} + 5xy - 36y = x^{2} + y(5x - 36) \] ### Step 3: Check for Further Factoring Next, see if the resulting expression can be factored further. The expression $$ x^{2} + y(5x - 36) $$ doesn't factor neatly into a product of binomials with integer coefficients. Therefore, it cannot be factored further using integer values. ### Final Factored Form \[ x^{2} + 5xy - 36y = x^{2} + y(5x - 36) \] ### Alternative Approach: Completing the Square or Using the Quadratic Formula If you're looking to solve for $$ x $$ in terms of $$ y $$, you can treat the expression as a quadratic equation: \[ x^{2} + 5xy - 36y = 0 \] Using the quadratic formula: \[ x = \frac{-5y \pm \sqrt{(5y)^2 + 4 \cdot 1 \cdot 36y}}{2} \] \[ x = \frac{-5y \pm \sqrt{25y^2 + 144y}}{2} \] \[ x = \frac{-5y \pm \sqrt{y(25y + 144)}}{2} \] This provides the solutions for $$ x $$ in terms of $$ y $$. --- If you have a specific goal in mind for this expression (such as solving for a variable, simplifying, or graphing), please provide more details, and I'd be happy to assist further! The expression $$ x^{2} + 5xy - 36y $$ can be factored as $$ x^{2} + y(5x - 36) $$. It cannot be factored further using integer values.

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$ x^{2}+5xy-36y $

Ask by Reeves Montgomery. in South Africa

Feb 03,2025

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The expression $ x^{2} + 5xy - 36y $ can be factored as $ x^{2} + y(5x - 36) $. It cannot be factored further using integer values.

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The expression $ x^{2}+5xy-36y $ can be factored by grouping. You can look for two numbers that multiply to $-36y$ (the constant term) and add up to $5y$ (the coefficient of $xy$). These numbers are $9y$ and $-4y$. Thus, you can rewrite the expression as $ x^2 + 9xy - 4xy - 36y $ and group it as $(x^2 + 9xy) + (-4xy - 36y)$. Factoring out common terms will lead you to $(x + 9y)(x - 4y)$. If you're ever stumped, remember that looking for factors of the constant that can be related to the coefficient can work wonders! A common mistake is forgetting to account for each term properly when grouping or overlooking negative signs, so double-check your addition and multiplication!

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