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

1. [tex]\(15x^7 + 10y^2\)[/tex]
- [tex]\(\boxed{5(3x^7 + 2y^2)}\)[/tex]

2. [tex]\(x^3(15x^4y^2 + 4)\)[/tex]
- [tex]\(\boxed{15x^7y^2 + 4x^3}\)[/tex]

3. [tex]\(15x^7y^2 + 3x\)[/tex]
- [tex]\(\boxed{3x(5x^6y^2 + 1)}\)[/tex]

4. [tex]\(15x^7y^2 + 4x^3\)[/tex]
- [tex]\(\boxed{x^3(15x^4y^2 + 4)}\)[/tex]

5. [tex]\(15x^7y^2 + 6xy\)[/tex]
- [tex]\(\boxed{3xy(5x^6y + 2)}\)[/tex]

Sagot :

GinnyAnsweridn
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]
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