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1. Factor común monomio:

Factorizar o descomponer en dos factores:

1. [tex]\(a^2 + a b\)[/tex]
2. [tex]\(b + b^2\)[/tex]
3. [tex]\(x^2 + x\)[/tex]
4. [tex]\(3a^3 - a^2\)[/tex]
5. [tex]\(x^3 - 4x^4\)[/tex]
6. [tex]\(5m^2 + 15m^3\)[/tex]
7. [tex]\(a b - b c\)[/tex]
8. [tex]\(x^2 y + x^2 z\)[/tex]
9. [tex]\(2a^2 x + 6a x^2\)[/tex]
10. [tex]\(8m^2 - 12m n\)[/tex]
11. [tex]\(9a^3 x^2 - 18a x^3\)[/tex]
12. [tex]\(15c^3 d^2 + 60c^2 d^3\)[/tex]
13. [tex]\(35m^2 n^3 - 70m^3\)[/tex]
14. [tex]\(a b c + a b c^2\)[/tex]
15. [tex]\(24a^2 x y^2 - 36x^2 y^4\)[/tex]
16. [tex]\(a^3 + a^2 + a\)[/tex]
17. [tex]\(4x^2 - 8x + 2\)[/tex]
18. [tex]\(15y^3 + 20y^2 - 5y\)[/tex]
19. [tex]\(a^3 - a^2 x + a x^2\)[/tex]

Sagot :

GinnyAnsweridn
Sure, let's factor each expression by finding the common monomial factor.

1) [tex]\(a^2 + a b\)[/tex]
- The common factor is [tex]\(a\)[/tex].
- Factored form: [tex]\(a(a + b)\)[/tex]

2) [tex]\(b + b^2\)[/tex]
- The common factor is [tex]\(b\)[/tex].
- Factored form: [tex]\(b(1 + b)\)[/tex]

3) [tex]\(x^2 + x\)[/tex]
- The common factor is [tex]\(x\)[/tex].
- Factored form: [tex]\(x(x + 1)\)[/tex]

4) [tex]\(3a^3 - a^2\)[/tex]
- The common factor is [tex]\(a^2\)[/tex].
- Factored form: [tex]\(a^2(3a - 1)\)[/tex]

5) [tex]\(x^3 - 4x^4\)[/tex]
- The common factor is [tex]\(x^3\)[/tex].
- Factored form: [tex]\(x^3(1 - 4x)\)[/tex]

6) [tex]\(5m^2 + 15m^3\)[/tex]
- The common factor is [tex]\(5m^2\)[/tex].
- Factored form: [tex]\(5m^2(1 + 3m)\)[/tex]

7) [tex]\(ab - bc\)[/tex]
- The common factor is [tex]\(b\)[/tex].
- Factored form: [tex]\(b(a - c)\)[/tex]

8) [tex]\(x^2 y + x^2 z\)[/tex]
- The common factor is [tex]\(x^2\)[/tex].
- Factored form: [tex]\(x^2(y + z)\)[/tex]

9) [tex]\(2a^2 x + 6a x^2\)[/tex]
- The common factor is [tex]\(2a x\)[/tex].
- Factored form: [tex]\(2a x(a + 3x)\)[/tex]

10) [tex]\(8m^2 - 12m n\)[/tex]
- The common factor is [tex]\(4m\)[/tex].
- Factored form: [tex]\(4m(2m - 3n)\)[/tex]

11) [tex]\(9a^3 x^2 - 18a x^3\)[/tex]
- The common factor is [tex]\(9a x^2\)[/tex].
- Factored form: [tex]\(9a x^2(a - 2x)\)[/tex]

12) [tex]\(15c^3 d^2 + 60c^2 d^3\)[/tex]
- The common factor is [tex]\(15c^2 d^2\)[/tex].
- Factored form: [tex]\(15c^2 d^2(c + 4d)\)[/tex]

13) [tex]\(35m^2 n^3 - 70m^3\)[/tex]
- The common factor is [tex]\(35m^2 n\)[/tex].
- Factored form: [tex]\(35m^2 n(n^2 - 2m)\)[/tex]

14) [tex]\(abc + abc^2\)[/tex]
- The common factor is [tex]\(abc\)[/tex].
- Factored form: [tex]\(abc(1 + c)\)[/tex]

15) [tex]\(24a^2 x y^2 - 36x^2 y^4\)[/tex]
- The common factor is [tex]\(12x y^2\)[/tex].
- Factored form: [tex]\(12x y^2(2a^2 - 3x y^2)\)[/tex]

16) [tex]\(a^3 + a^2 + a\)[/tex]
- The common factor is [tex]\(a\)[/tex].
- Factored form: [tex]\(a(a^2 + a + 1)\)[/tex]

17) [tex]\(4x^2 - 8x + 2\)[/tex]
- The common factor is [tex]\(2\)[/tex].
- Factored form: [tex]\(2(2x^2 - 4x + 1)\)[/tex]

18) [tex]\(15y^3 + 20y^2 - 5y\)[/tex]
- The common factor is [tex]\(5y\)[/tex].
- Factored form: [tex]\(5y(3y^2 + 4y - 1)\)[/tex]

19) [tex]\(a^3 - a^2 x + a x^2\)[/tex]
- The common factor is [tex]\(a\)[/tex].
- Factored form: [tex]\(a(a^2 - a x + x^2)\)[/tex]

These are the factored forms of the given expressions by extracting the common monomial factor.