IDNLearn.com provides a platform for sharing and gaining valuable knowledge. Discover in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
Sure, let's factorize the given expression step-by-step.
The given expression is:
[tex]\[ x^2 + 6xy + 9y^2 \][/tex]
Notice that the expression is a quadratic trinomial. To factorize it, we need to look for two binomials (in the form of [tex]\((ax + by)(cx + dy)\)[/tex]) whose product gives us the original quadratic trinomial.
1. Identify the first and the last term:
- The first term is [tex]\(x^2\)[/tex], which is [tex]\((x)(x)\)[/tex].
- The last term is [tex]\(9y^2\)[/tex], which is [tex]\((3y)(3y)\)[/tex].
2. Identify the middle term:
- The middle term is [tex]\(6xy\)[/tex].
3. Validate our factorization by checking the middle term:
- When we look at the possible binomials, we notice that if we use [tex]\((x + 3y)(x + 3y)\)[/tex], we need to check if this product gives us the correct middle term.
Now let's expand [tex]\((x + 3y)^2\)[/tex] to check if it matches the original expression:
[tex]\[ (x + 3y)(x + 3y) = x(x + 3y) + 3y(x + 3y) \][/tex]
4. Distribute [tex]\(x\)[/tex] and [tex]\(3y\)[/tex]:
- [tex]\(x(x + 3y) = x^2 + 3xy\)[/tex]
- [tex]\(3y(x + 3y) = 3xy + 9y^2\)[/tex]
5. Combine like terms:
- [tex]\(x^2 + 3xy + 3xy + 9y^2 = x^2 + 6xy + 9y^2\)[/tex]
We can see that the expansion of [tex]\((x + 3y)^2\)[/tex] gives us back the original expression [tex]\(x^2 + 6xy + 9y^2\)[/tex].
Hence, the factorized form of the given expression is:
[tex]\[ (x + 3y)^2 \][/tex]
The given expression is:
[tex]\[ x^2 + 6xy + 9y^2 \][/tex]
Notice that the expression is a quadratic trinomial. To factorize it, we need to look for two binomials (in the form of [tex]\((ax + by)(cx + dy)\)[/tex]) whose product gives us the original quadratic trinomial.
1. Identify the first and the last term:
- The first term is [tex]\(x^2\)[/tex], which is [tex]\((x)(x)\)[/tex].
- The last term is [tex]\(9y^2\)[/tex], which is [tex]\((3y)(3y)\)[/tex].
2. Identify the middle term:
- The middle term is [tex]\(6xy\)[/tex].
3. Validate our factorization by checking the middle term:
- When we look at the possible binomials, we notice that if we use [tex]\((x + 3y)(x + 3y)\)[/tex], we need to check if this product gives us the correct middle term.
Now let's expand [tex]\((x + 3y)^2\)[/tex] to check if it matches the original expression:
[tex]\[ (x + 3y)(x + 3y) = x(x + 3y) + 3y(x + 3y) \][/tex]
4. Distribute [tex]\(x\)[/tex] and [tex]\(3y\)[/tex]:
- [tex]\(x(x + 3y) = x^2 + 3xy\)[/tex]
- [tex]\(3y(x + 3y) = 3xy + 9y^2\)[/tex]
5. Combine like terms:
- [tex]\(x^2 + 3xy + 3xy + 9y^2 = x^2 + 6xy + 9y^2\)[/tex]
We can see that the expansion of [tex]\((x + 3y)^2\)[/tex] gives us back the original expression [tex]\(x^2 + 6xy + 9y^2\)[/tex].
Hence, the factorized form of the given expression is:
[tex]\[ (x + 3y)^2 \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.