7 Read what Mia says. When I expand and simplify $$ x(x-3)+x(x+5) $$, I get the same answer as when I expand $$ 2 x(x+1) $$. Is Mia correct? Explain your answer.

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UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$2x\left(x+1\right)$$
- step1: Apply the distributive property:
  $$2x\times x+2x\times 1$$
- step2: Multiply the terms:
  $$2x^{2}+2x$$
Expand the expression $$ x(x-3)+x(x+5) $$
Simplify the expression by following steps:
- step0: Add the terms:
  $$x\left(x-3\right)+x\left(x+5\right)$$
- step1: Expand the expression:
  $$x^{2}-3x+x\left(x+5\right)$$
- step2: Expand the expression:
  $$x^{2}-3x+x^{2}+5x$$
- step3: Add the terms:
  $$2x^{2}+2x$$
Let's analyze Mia's statement step by step.

1. **Expanding and simplifying $$ x(x-3) + x(x+5) $$**:
   - First, we expand each term:
     - $$ x(x-3) = x^2 - 3x $$
     - $$ x(x+5) = x^2 + 5x $$
   - Now, we combine these:
     $$
     x^2 - 3x + x^2 + 5x = 2x^2 + 2x
     $$

2. **Expanding $$ 2x(x+1) $$**:
   - We expand this term:
     - $$ 2x(x+1) = 2x^2 + 2x $$

3. **Comparison**:
   - Both expressions simplify to $$ 2x^2 + 2x $$.

Since both expansions yield the same result, Mia is correct. The expanded forms of $$ x(x-3) + x(x+5) $$ and $$ 2x(x+1) $$ are indeed equal.
Mia is correct because both expressions simplify to $$ 2x^2 + 2x $$.

7 Read what Mia says. When I expand and simplify \( x(x-3)+x(x+5) \), I get the same answer as when I expand \( 2 x(x+1) \). Is Mia correct? Explain your answer.

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