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Sagot :
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.
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.
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