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

1. [tex]15x^7 y^2 + 4x^3[/tex]

2. [tex]15x^7 + 10y^2[/tex]

3. [tex]15x^7 y^2 + 3x[/tex]

4. [tex]15x^7 y^2 + 6xy[/tex]

A. [tex]x^3(15x^4 y^2 + 4)[/tex]

B. [tex]3xy(5x^6 y + 2)[/tex]

C. [tex]3x(5x^6 y^2 + 1)[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's match each given expression in standard form with its equivalent factored form.

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

Matching factored form: [tex]\( x^3(15 x^4 y^2 + 4) \)[/tex]

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

Matching factored form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]

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

Matching factored form: [tex]\( 3x(5 x^6 y^2 + 1) \)[/tex]

4. Expression in standard form: [tex]\( 15 x^7 y^2 + 6 x y \)[/tex]

Matching factored form: [tex]\( 3xy(5 x^6 y + 2) \)[/tex]

5. Factored expression: [tex]\( x^3(15 x^4 y^2 + 4) \)[/tex]

Matching standard form: [tex]\( 15 x^7 y^2 + 4 x^3 \)[/tex]

6. Factored expression: [tex]\( 3xy(5 x^6 y + 2) \)[/tex]

Matching standard form: [tex]\( 15 x^7 y^2 + 6 x y \)[/tex]

7. Factored expression: [tex]\( 3x(5 x^6 y^2 + 1) \)[/tex]

Matching standard form: [tex]\( 15 x^7 y^2 + 3 x \)[/tex]

Thus, the matches are:

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

These are the equivalent expressions in their factored and standard forms matched correctly.
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