Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Of course! Let's multiply the expressions [tex]\((x^2 - 2xy)\)[/tex] and [tex]\((3xy + y^2)\)[/tex] step by step.
### Step-by-Step Multiplication
1. Distribute [tex]\( x^2 \)[/tex] across [tex]\(3xy + y^2\)[/tex]:
[tex]\[ x^2 \cdot (3xy + y^2) = x^2 \cdot 3xy + x^2 \cdot y^2 \][/tex]
This gives:
[tex]\[ 3x^3y + x^2y^2 \][/tex]
2. Distribute [tex]\(-2xy\)[/tex] across [tex]\(3xy + y^2\)[/tex]:
[tex]\[ -2xy \cdot (3xy + y^2) = -2xy \cdot 3xy - 2xy \cdot y^2 \][/tex]
This gives:
[tex]\[ -6x^2y^2 - 2xy^3 \][/tex]
3. Combine all the terms together:
[tex]\[ 3x^3y + x^2y^2 - 6x^2y^2 - 2xy^3 \][/tex]
4. Simplify by combining like terms:
[tex]\[ 3x^3y + (x^2y^2 - 6x^2y^2) - 2xy^3 \][/tex]
[tex]\[ 3x^3y - 5x^2y^2 - 2xy^3 \][/tex]
### Final Result
Therefore, the result of multiplying [tex]\((x^2 - 2xy)\)[/tex] by [tex]\((3xy + y^2)\)[/tex] is:
[tex]\[ 3x^3y - 5x^2y^2 - 2xy^3 \][/tex]
### Step-by-Step Multiplication
1. Distribute [tex]\( x^2 \)[/tex] across [tex]\(3xy + y^2\)[/tex]:
[tex]\[ x^2 \cdot (3xy + y^2) = x^2 \cdot 3xy + x^2 \cdot y^2 \][/tex]
This gives:
[tex]\[ 3x^3y + x^2y^2 \][/tex]
2. Distribute [tex]\(-2xy\)[/tex] across [tex]\(3xy + y^2\)[/tex]:
[tex]\[ -2xy \cdot (3xy + y^2) = -2xy \cdot 3xy - 2xy \cdot y^2 \][/tex]
This gives:
[tex]\[ -6x^2y^2 - 2xy^3 \][/tex]
3. Combine all the terms together:
[tex]\[ 3x^3y + x^2y^2 - 6x^2y^2 - 2xy^3 \][/tex]
4. Simplify by combining like terms:
[tex]\[ 3x^3y + (x^2y^2 - 6x^2y^2) - 2xy^3 \][/tex]
[tex]\[ 3x^3y - 5x^2y^2 - 2xy^3 \][/tex]
### Final Result
Therefore, the result of multiplying [tex]\((x^2 - 2xy)\)[/tex] by [tex]\((3xy + y^2)\)[/tex] is:
[tex]\[ 3x^3y - 5x^2y^2 - 2xy^3 \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.