Answer :
The expression [tex]9x^4-64y^2[/tex] is factored into [tex](3x^2 - 8y) * (3x^2 + 8y)[/tex] by applying the difference of squares formula.
The expression you're trying to factor is [tex]9x^4-64y^2[/tex]
We can approach this problem by recognizing that this is a Factoring difference of squares, which can be factored as follows:
Step 1:
Balance the equation as [tex]a^2 - b^2[/tex] where [tex]a=\sqrt{(9x^4)[/tex] and [tex]b=\sqrt{(64y^2)[/tex]
This satisfies the equation. [tex]a^2 = 9x^4[/tex], where [tex]a = 3x^2[/tex], and [tex]b^2 = 64y^2[/tex], where b=8y.
This leads us to [tex](3x^2)^2 - (8y)^2.[/tex]
Step 2:
Apply the difference of squares formula: [tex]a^2 - b^2[/tex] = (a - b) * (a + b)
In our case, [tex]a = 3x^2[/tex], and b = 8y, so we substitute these back into our equation to obtain: [tex](3x^2 - 8y) * (3x^2 + 8y)[/tex].
This is the factored form of the original expression.
Learn more about Factoring difference of squares here:
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Answer:
(3x² + 8y)(3x² - 8y)
Step-by-step explanation:
9x^4 - 64y^2
~Rewrite
(3x²)² - (8y)²
~Apply difference of two squares
(3x² + 8y)(3x² - 8y)
Best of Luck!
