代数运算解析：展开与合并表达式
开心田螺
2025-02-24 16:00:03
0次
It seems like you're trying to expand or simplify an algebraic expression, but the expression is not clearly formatted. Based on what you've provided, I'll assume you want to simplify or expand the following expression:
\[
(3x - y)(3x + y) + y(x + y)
\]
Let's break it down step by step.
### Step 1: Expand \((3x - y)(3x + y)\)
This is a difference of squares:
\[
(3x - y)(3x + y) = (3x)^2 - (y)^2 = 9x^2 - y^2
\]
### Step 2: Expand \(y(x + y)\)
Distribute \(y\) across the terms inside the parentheses:
\[
y(x + y) = y \cdot x + y \cdot y = xy + y^2
\]
### Step 3: Combine the results
Now, add the results from steps 1 and 2:
\[
9x^2 - y^2 + xy + y^2
\]
Notice that \(-y^2\) and \(+y^2\) cancel each other out:
\[
9x^2 + xy
\]
So, the simplified expression is:
\[
9x^2 + xy
\]
\[
(3x - y)(3x + y) + y(x + y)
\]
Let's break it down step by step.
### Step 1: Expand \((3x - y)(3x + y)\)
This is a difference of squares:
\[
(3x - y)(3x + y) = (3x)^2 - (y)^2 = 9x^2 - y^2
\]
### Step 2: Expand \(y(x + y)\)
Distribute \(y\) across the terms inside the parentheses:
\[
y(x + y) = y \cdot x + y \cdot y = xy + y^2
\]
### Step 3: Combine the results
Now, add the results from steps 1 and 2:
\[
9x^2 - y^2 + xy + y^2
\]
Notice that \(-y^2\) and \(+y^2\) cancel each other out:
\[
9x^2 + xy
\]
So, the simplified expression is:
\[
9x^2 + xy
\]
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