Sure, let's solve and simplify the expression [tex]\(2x^2(x + y) - 3(x + y)\)[/tex] step-by-step.
1. Distribute the terms inside the expressions:
- For the term [tex]\(2x^2(x + y)\)[/tex]:
- Distribute [tex]\(2x^2\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
2x^2 \cdot x + 2x^2 \cdot y
\][/tex]
This simplifies to:
[tex]\[
2x^3 + 2x^2y
\][/tex]
- For the term [tex]\(-3(x + y)\)[/tex]:
- Distribute [tex]\(-3\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
-3 \cdot x + -3 \cdot y
\][/tex]
This simplifies to:
[tex]\[
-3x - 3y
\][/tex]
2. Combine all the resulting terms:
- Combine the terms we have from the expanded expressions:
[tex]\[
2x^3 + 2x^2y - 3x - 3y
\][/tex]
So, the simplified form of the given expression [tex]\(2x^2(x + y) - 3(x + y)\)[/tex] is:
[tex]\[
2x^3 + 2x^2y - 3x - 3y
\][/tex]
