Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Sure, let's solve the expression [tex]\((3x + 2y)(5x^2 + 2xy - 4y^2)\)[/tex] step-by-step.
We will use the distributive property to expand this expression.
1. First, distribute each term in the first parenthesis [tex]\((3x + 2y)\)[/tex] to each term in the second parenthesis [tex]\((5x^2 + 2xy - 4y^2)\)[/tex].
[tex]\[ (3x + 2y)(5x^2 + 2xy - 4y^2) \][/tex]
This can be broken down into:
[tex]\[ 3x(5x^2 + 2xy - 4y^2) + 2y(5x^2 + 2xy - 4y^2) \][/tex]
2. Now, distribute [tex]\(3x\)[/tex] to each term inside the parentheses first:
[tex]\[ 3x \cdot 5x^2 = 15x^3 \][/tex]
[tex]\[ 3x \cdot 2xy = 6x^2y \][/tex]
[tex]\[ 3x \cdot (-4y^2) = -12xy^2 \][/tex]
So, the first part simplifies to:
[tex]\[ 15x^3 + 6x^2y - 12xy^2 \][/tex]
3. Next, distribute [tex]\(2y\)[/tex] to each term inside the parentheses:
[tex]\[ 2y \cdot 5x^2 = 10x^2y \][/tex]
[tex]\[ 2y \cdot 2xy = 4xy^2 \][/tex]
[tex]\[ 2y \cdot (-4y^2) = -8y^3 \][/tex]
So, the second part simplifies to:
[tex]\[ 10x^2y + 4xy^2 - 8y^3 \][/tex]
4. Combine the results from both parts:
[tex]\[ 15x^3 + 6x^2y - 12xy^2 + 10x^2y + 4xy^2 - 8y^3 \][/tex]
5. Combine like terms:
Combine terms involving [tex]\(x^2y\)[/tex]:
[tex]\[ 6x^2y + 10x^2y = 16x^2y \][/tex]
Combine terms involving [tex]\(xy^2\)[/tex]:
[tex]\[ -12xy^2 + 4xy^2 = -8xy^2 \][/tex]
So, the expression simplifies to:
[tex]\[ 15x^3 + 16x^2y - 8xy^2 - 8y^3 \][/tex]
Therefore, the expanded form of the expression [tex]\((3x + 2y)(5x^2 + 2xy - 4y^2)\)[/tex] is:
[tex]\[ 15x^3 + 16x^2y - 8xy^2 - 8y^3 \][/tex]
We will use the distributive property to expand this expression.
1. First, distribute each term in the first parenthesis [tex]\((3x + 2y)\)[/tex] to each term in the second parenthesis [tex]\((5x^2 + 2xy - 4y^2)\)[/tex].
[tex]\[ (3x + 2y)(5x^2 + 2xy - 4y^2) \][/tex]
This can be broken down into:
[tex]\[ 3x(5x^2 + 2xy - 4y^2) + 2y(5x^2 + 2xy - 4y^2) \][/tex]
2. Now, distribute [tex]\(3x\)[/tex] to each term inside the parentheses first:
[tex]\[ 3x \cdot 5x^2 = 15x^3 \][/tex]
[tex]\[ 3x \cdot 2xy = 6x^2y \][/tex]
[tex]\[ 3x \cdot (-4y^2) = -12xy^2 \][/tex]
So, the first part simplifies to:
[tex]\[ 15x^3 + 6x^2y - 12xy^2 \][/tex]
3. Next, distribute [tex]\(2y\)[/tex] to each term inside the parentheses:
[tex]\[ 2y \cdot 5x^2 = 10x^2y \][/tex]
[tex]\[ 2y \cdot 2xy = 4xy^2 \][/tex]
[tex]\[ 2y \cdot (-4y^2) = -8y^3 \][/tex]
So, the second part simplifies to:
[tex]\[ 10x^2y + 4xy^2 - 8y^3 \][/tex]
4. Combine the results from both parts:
[tex]\[ 15x^3 + 6x^2y - 12xy^2 + 10x^2y + 4xy^2 - 8y^3 \][/tex]
5. Combine like terms:
Combine terms involving [tex]\(x^2y\)[/tex]:
[tex]\[ 6x^2y + 10x^2y = 16x^2y \][/tex]
Combine terms involving [tex]\(xy^2\)[/tex]:
[tex]\[ -12xy^2 + 4xy^2 = -8xy^2 \][/tex]
So, the expression simplifies to:
[tex]\[ 15x^3 + 16x^2y - 8xy^2 - 8y^3 \][/tex]
Therefore, the expanded form of the expression [tex]\((3x + 2y)(5x^2 + 2xy - 4y^2)\)[/tex] is:
[tex]\[ 15x^3 + 16x^2y - 8xy^2 - 8y^3 \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.