lucia finds that $(3x^{2}+3x + 5)+(7x^{2}-9x + 8)=10x^{2}-12x + 13$. what error did lucia make?\nshe found…

lucia finds that $(3x^{2}+3x + 5)+(7x^{2}-9x + 8)=10x^{2}-12x + 13$. what error did lucia make?\nshe found the difference instead of the sum.\nshe combined the terms $3x^{2}$ and $7x^{2}$ incorrectly.\nshe combined the terms $3x$ and $-9x$ incorrectly.\nshe did not combine all like terms.

lucia finds that $(3x^{2}+3x + 5)+(7x^{2}-9x + 8)=10x^{2}-12x + 13$. what error did lucia make?\nshe found the difference instead of the sum.\nshe combined the terms $3x^{2}$ and $7x^{2}$ incorrectly.\nshe combined the terms $3x$ and $-9x$ incorrectly.\nshe did not combine all like terms.

Answer

Explanation:

Step1: Combine like - terms

First, combine the $x^{2}$ terms: $(3x^{2}+7x^{2}) = 10x^{2}$. Then, combine the $x$ terms: $(3x-9x)=3x+( - 9x)=-6x$. And combine the constant terms: $(5 + 8)=13$. So, $(3x^{2}+3x + 5)+(7x^{2}-9x + 8)=10x^{2}-6x + 13$.

Step2: Analyze Lucia's work

Lucia got $10x^{2}-12x + 13$. The error is in combining the $x$ - terms. She incorrectly calculated $3x-9x$ as $-12x$ instead of $-6x$.

Answer:

She combined the terms $3x$ and $-9x$ incorrectly.