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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]



Answer :

GinnyAnswer
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]

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