Final answer:
The given expression x(3x - 2) + x(5x + 7) is expanded using the distributive property to get 3x² - 2x + 5x² + 7x, then simplified by combining like terms to get 8x² + 5x.
Step-by-step explanation:
To expand and simplify the given expression, we need to apply the distributive property, which involves multiplying each term inside the parenthesis by the term outside. Here's the step-by-step expansion:
- Multiply x by 3x to get 3x².
- Multiply x by -2 to get -2x.
- Multiply x by 5x to get 5x².
- Multiply x by 7 to get 7x.
Combine all the terms to get the simplified expression: 3x² - 2x + 5x² + 7x.
Now, combine like terms:
- Add 3x² and 5x² to get 8x².
- Add -2x and 7x to get 5x.
Thus, the expanded and simplified form of the expression is 8x² + 5x.
After expanding, we eliminate terms wherever possible to simplify the algebra, and then we check the answer to see if it is reasonable.