Answer :
To factor the expression [tex]$$27x^2 + 36x,$$[/tex] we first look for the greatest common factor (GCF) of the two terms.
1. Both coefficients, 27 and 36, have a common factor of 9.
2. Each term also contains a factor of [tex]$$x.$$[/tex]
Thus, the GCF is [tex]$$9x.$$[/tex]
Now, we factor out [tex]$$9x$$[/tex] from the expression:
[tex]$$
27x^2 + 36x = 9x\left(\frac{27x^2}{9x} + \frac{36x}{9x}\right).
$$[/tex]
Simplify each term inside the parentheses:
- [tex]$$\frac{27x^2}{9x} = 3x,$$[/tex]
- [tex]$$\frac{36x}{9x} = 4.$$[/tex]
So, the expression becomes:
[tex]$$
27x^2 + 36x = 9x(3x + 4).
$$[/tex]
Thus, the factored form of the expression is [tex]$$\boxed{9x(3x+4)}.$$[/tex]
1. Both coefficients, 27 and 36, have a common factor of 9.
2. Each term also contains a factor of [tex]$$x.$$[/tex]
Thus, the GCF is [tex]$$9x.$$[/tex]
Now, we factor out [tex]$$9x$$[/tex] from the expression:
[tex]$$
27x^2 + 36x = 9x\left(\frac{27x^2}{9x} + \frac{36x}{9x}\right).
$$[/tex]
Simplify each term inside the parentheses:
- [tex]$$\frac{27x^2}{9x} = 3x,$$[/tex]
- [tex]$$\frac{36x}{9x} = 4.$$[/tex]
So, the expression becomes:
[tex]$$
27x^2 + 36x = 9x(3x + 4).
$$[/tex]
Thus, the factored form of the expression is [tex]$$\boxed{9x(3x+4)}.$$[/tex]
