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$Use your result from the previous task to find the sum. $ 6 a b^{2} $ $ 3 a b+3 b^{2} $ $ \left.b^{2}\right)-6 a^{2}+3 a b+3 b^{2} $ \( -6 a^{2}-13 a b+3$

Use your result from the previous task to find the sum. $ 6 a b^{2} $ $ 3 a b+3 b^{2} $ $ \left.b^{2}\right)-6 a^{2}+3 a b+3 b^{2} $ $ -6 a^{2}-13 a b+3 b^{2} $ DONE

Ask by Malone Erickson.

Feb 06,2025 22:59

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Tutor-Verified Answer

Answer

The sum of the expressions is $ -6a^{2} - 13ab + 3b^{2} $.

Solution

Based on the expressions you've provided, let's verify the sum step by step: 1. **First Expression:** \[ 6 a b^{2} \] 2. **Second Expression:** \[ 3 a b + 3 b^{2} \] 3. **Third Expression:** \[ -6 a^{2} + 3 a b + 3 b^{2} \] 4. **Final Sum:** \[ -6 a^{2} - 13 a b + 3 b^{2} \] **Summing All Expressions:** Let's add them all together: \[ 6 a b^{2} + (3 a b + 3 b^{2}) + (-6 a^{2} + 3 a b + 3 b^{2}) = -6 a^{2} - 13 a b + 3 b^{2} \] **Final Result:** \[ -6 a^{2} - 13 a b + 3 b^{2} \] If you have any further questions or need additional assistance, feel free to ask!

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The Deep Dive

To find the sum of the given expressions, first, we combine them step by step: 1. $6ab^2$ 2. $3ab + 3b^2$ 3. $b^2 - 6a^2 + 3ab + 3b^2$ 4. $-6a^2 - 13ab + 3b^2$ Now let's add them together: Combine all like terms: - Terms involving $a^2$: $-6a^2 - 6a^2 = -12a^2$ - Terms involving $ab$: $6ab^2 + 3ab + 3ab - 13ab = -1ab$ - Terms involving $b^2$: $6ab^2 + 3b^2 + 3b^2 + b^2 = 13b^2$ Putting it all together, the sum is: $-12a^2 - ab + 13b^2$ And that's your final combined expression.