Question
Expand the brackets for the following algebraic expression: \[ 6 x^{7} y^{2}\left(3 x^{4} y+5 x y^{6}\right) \]
Ask by Rowe Chadwick. in South Africa
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expanded form of the expression is \(18x^{11}y^{3} + 30x^{8}y^{8}\).
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The Deep Dive
When expanding the brackets for the expression \( 6 x^{7} y^{2}\left(3 x^{4} y+5 x y^{6}\right) \), you need to distribute \( 6 x^{7} y^{2} \) to both terms inside the parentheses. First, we multiply: 1. \( 6 x^{7} y^{2} \cdot 3 x^{4} y = 18 x^{11} y^{3} \) 2. \( 6 x^{7} y^{2} \cdot 5 x y^{6} = 30 x^{8} y^{8} \) Now, we combine both results: \[ 18 x^{11} y^{3} + 30 x^{8} y^{8} \] So, the final expanded expression is: \[ 18 x^{11} y^{3} + 30 x^{8} y^{8} \]