Answer :
Certainly! Let's match each expression in standard form with its equivalent expression in factored form.
1. Expression in standard form: [tex]\( 15 x^7 + 10 y^2 \)[/tex]
- Equivalent factored form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]
2. Expression in standard form: [tex]\( x^3\left(15 x^4 y^2 + 4\right) \)[/tex]
- Equivalent factored form: [tex]\( x^3\left(15 x^4 y^2 + 4\right) \)[/tex] (This expression is already in factored form)
3. Expression in standard form: [tex]\( 15 x^7 y^2 + 3 x \)[/tex]
- Equivalent factored form: [tex]\( 3 x\left(5 x^6 y^2 + 1\right) \)[/tex]
4. Expression in standard form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]
- Equivalent factored form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex] (This expression is already in factored form)
5. Expression in standard form: [tex]\( 15 x^7 y^2 + 4 x^3 \)[/tex]
- Equivalent factored form: [tex]\( x^3(15 x^4 y^2 + 4) \)[/tex]
6. Expression in standard form: [tex]\( 3 x y\left(5 x^6 y + 2\right) \)[/tex]
- Equivalent factored form: [tex]\( 3 x y(5 x^6 y + 2) \)[/tex] (This expression is already in factored form)
7. Expression in standard form: [tex]\( 15 x^7 y^2 + 6 x y \)[/tex]
- Equivalent factored form: [tex]\( 3 x y(5 x^6 y + 2) \)[/tex]
8. Expression in standard form: [tex]\( 3 x\left(5 x^6 y^2 + 1\right) \)[/tex]
- Equivalent factored form: [tex]\( 3 x(5 x^6 y^2 + 1) \)[/tex] (This expression is already in factored form)
Thus, the matching is as follows:
[tex]\[ \begin{align*} 15 x^7 + 10 y^2 & \quad \text{matches with} \quad 5(3 x^7 + 2 y^2) \\ x^3\left(15 x^4 y^2 + 4\right) & \quad \text{matches with} \quad x^3\left(15 x^4 y^2 + 4\right) \\ 15 x^7 y^2 + 3 x & \quad \text{matches with} \quad 3 x\left(5 x^6 y^2 + 1\right) \\ 5(3 x^7 + 2 y^2) & \quad \text{matches with} \quad 5(3 x^7 + 2 y^2) \\ 15 x^7 y^2 + 4 x^3 & \quad \text{matches with} \quad x^3(15 x^4 y^2 + 4) \\ 3 x y\left(5 x^6 y + 2\right) & \quad \text{matches with} \quad 3 x y(5 x^6 y + 2) \\ 15 x^7 y^2 + 6 x y & \quad \text{matches with} \quad 3 x y(5 x^6 y + 2) \\ 3 x\left(5 x^6 y^2 + 1\right) & \quad \text{matches with} \quad 3 x(5 x^6 y^2 + 1) \end{align*} \][/tex]
1. Expression in standard form: [tex]\( 15 x^7 + 10 y^2 \)[/tex]
- Equivalent factored form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]
2. Expression in standard form: [tex]\( x^3\left(15 x^4 y^2 + 4\right) \)[/tex]
- Equivalent factored form: [tex]\( x^3\left(15 x^4 y^2 + 4\right) \)[/tex] (This expression is already in factored form)
3. Expression in standard form: [tex]\( 15 x^7 y^2 + 3 x \)[/tex]
- Equivalent factored form: [tex]\( 3 x\left(5 x^6 y^2 + 1\right) \)[/tex]
4. Expression in standard form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex]
- Equivalent factored form: [tex]\( 5(3 x^7 + 2 y^2) \)[/tex] (This expression is already in factored form)
5. Expression in standard form: [tex]\( 15 x^7 y^2 + 4 x^3 \)[/tex]
- Equivalent factored form: [tex]\( x^3(15 x^4 y^2 + 4) \)[/tex]
6. Expression in standard form: [tex]\( 3 x y\left(5 x^6 y + 2\right) \)[/tex]
- Equivalent factored form: [tex]\( 3 x y(5 x^6 y + 2) \)[/tex] (This expression is already in factored form)
7. Expression in standard form: [tex]\( 15 x^7 y^2 + 6 x y \)[/tex]
- Equivalent factored form: [tex]\( 3 x y(5 x^6 y + 2) \)[/tex]
8. Expression in standard form: [tex]\( 3 x\left(5 x^6 y^2 + 1\right) \)[/tex]
- Equivalent factored form: [tex]\( 3 x(5 x^6 y^2 + 1) \)[/tex] (This expression is already in factored form)
Thus, the matching is as follows:
[tex]\[ \begin{align*} 15 x^7 + 10 y^2 & \quad \text{matches with} \quad 5(3 x^7 + 2 y^2) \\ x^3\left(15 x^4 y^2 + 4\right) & \quad \text{matches with} \quad x^3\left(15 x^4 y^2 + 4\right) \\ 15 x^7 y^2 + 3 x & \quad \text{matches with} \quad 3 x\left(5 x^6 y^2 + 1\right) \\ 5(3 x^7 + 2 y^2) & \quad \text{matches with} \quad 5(3 x^7 + 2 y^2) \\ 15 x^7 y^2 + 4 x^3 & \quad \text{matches with} \quad x^3(15 x^4 y^2 + 4) \\ 3 x y\left(5 x^6 y + 2\right) & \quad \text{matches with} \quad 3 x y(5 x^6 y + 2) \\ 15 x^7 y^2 + 6 x y & \quad \text{matches with} \quad 3 x y(5 x^6 y + 2) \\ 3 x\left(5 x^6 y^2 + 1\right) & \quad \text{matches with} \quad 3 x(5 x^6 y^2 + 1) \end{align*} \][/tex]