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.
