Answer:
[tex]\left(a + \dfrac{b}{3}\right) \left(a - \dfrac{b}{3}\right)[/tex]
Step-by-step explanation:
The given expression is
[tex]4a^2 - \dfrac{1}{9}b^2[/tex]
To expand this expression we will use the difference of squares formula which states
[tex]x^2 - y^2 = (x + y)(x -y)[/tex]
Comparing the given expression and the right side of the formula we see
- [tex]x^2 = 4a^2 \rightarrow x = \sqrt{4a^2} = 2a[/tex]
- [tex]y^2 = \sqrt{\dfrac{1}{9}b^2} \rightarrow b = \dfrac{1}{3}b[/tex]
Therefore,
[tex]$\quad 4a^2 - \dfrac{1}{9}b^2 = \left(2a + \dfrac{1}{3}b\right)\left(2a - \dfrac{1}{3}b\right)\\\\$[/tex]
or, equivalently
[tex]\qquad 4a^2 - \dfrac{1}{9}b^2 = \left(a + \dfrac{b}{3}\right) \left(a - \dfrac{b}{3}\right)$[/tex]
