Answered

Get the information you need from a community of experts on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

Match each expression written in standard form to the equivalent expression in factored form.

1. [tex]\(15 x^7 y^2 + 6 x y\)[/tex]
2. [tex]\(15 x^7 y^2 + 3 x\)[/tex]
3. [tex]\(15 x^7 y^2 + 4 x^3\)[/tex]
4. [tex]\(15 x^7 + 10 y^2\)[/tex]

A. [tex]\(x^3\left(15 x^4 y^2 + 4\right)\)[/tex]
B. [tex]\(3 x y\left(5 x^6 y + 2\right)\)[/tex]
C. [tex]\(3 x \left(5 x^6 y^2 + 1\right)\)[/tex]
D. [tex]\(5\left(3 x^7 + 2 y^2\right)\)[/tex]

Sagot :

GinnyAnsweridn
Let's match each standard form expression to its corresponding factored form step by step:

1. Expression: [tex]\( 15x^7 y^2 + 6xy \)[/tex]

Factored form:
Let's break down the terms of the expression and look for common factors.
Both terms [tex]\( 15x^7y^2 \)[/tex] and [tex]\( 6xy \)[/tex] have [tex]\( xy \)[/tex] as a common factor.
Therefore, [tex]\( 15x^7y^2 + 6xy = xy(15x^6y + 6) \)[/tex].

2. Expression: [tex]\( 15x^7 + 10y^2 \)[/tex]

Factored form:
Let's break down the terms of the expression and look for common factors.
Both terms [tex]\( 15x^7 \)[/tex] and [tex]\( 10y^2 \)[/tex] have [tex]\( 5 \)[/tex] as a common factor.
Therefore, [tex]\( 15x^7 + 10y^2 = 5(3x^7 + 2y^2) \)[/tex].

3. Expression: [tex]\( 15x^7y^2 + 3x \)[/tex]

Factored form:
Let's break down the terms of the expression and look for common factors.
Both terms [tex]\( 15x^7y^2 \)[/tex] and [tex]\( 3x \)[/tex] have [tex]\( 3x \)[/tex] as a common factor.
Therefore, [tex]\( 15x^7y^2 + 3x = 3x(5x^6y^2 + 1) \)[/tex].

4. Expression: [tex]\( 15x^7y^2 + 4x^3 \)[/tex]

Factored form:
Let's break down the terms of the expression and look for common factors.
Both terms [tex]\( 15x^7y^2 \)[/tex] and [tex]\( 4x^3 \)[/tex] have [tex]\( x^3 \)[/tex] as a common factor.
Therefore, [tex]\( 15x^7y^2 + 4x^3 = x^3(15x^4y^2 + 4) \)[/tex].

Now, we can match each standard form expression with its factored form:

- [tex]\( 15x^7 y^2 + 6xy \)[/tex] matches with [tex]\( 3xy(5x^6y + 2) \)[/tex]
- [tex]\( 15x^7 + 10y^2 \)[/tex] matches with [tex]\( 5(3x^7 + 2y^2) \)[/tex]
- [tex]\( 15x^7 y^2 + 3x \)[/tex] matches with [tex]\( 3x(5x^6y^2 + 1) \)[/tex]
- [tex]\( 15x^7 y^2 + 4x^3 \)[/tex] matches with [tex]\( x^3(15x^4y^2 + 4) \)[/tex]

In summary, here's the detailed matching:

1. [tex]\( 15 x^7 y^2 + 6xy \)[/tex] matches with [tex]\( 3xy(5 x^6 y + 2) \)[/tex]
2. [tex]\( 15 x^7 + 10 y^2 \)[/tex] matches with [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]
3. [tex]\( 15 x^7 y^2 + 3 x \)[/tex] matches with [tex]\( 3 x(5 x^6 y^2 + 1) \)[/tex]
4. [tex]\( 15 x^7 y^2 + 4 x^3 \)[/tex] matches with [tex]\( x^3(15 x^4 y^2 + 4) \)[/tex]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.