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4a²-1/9b² (expand it)​

Sagot :

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]

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