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Answer :
Final answer:
To factor the expression completely, we can use the difference of squares formula and then further factor if necessary.
Explanation:
To factor the expression 81xâ´ - 625yâ´ completely, we can use the difference of squares formula. The formula states that a² - b² can be factored as (a + b)(a - b). In this case, 81xâ´ is the square of 9x² and 625yâ´ is the square of 25y². Therefore, we have:
81xâ´ - 625yâ´ = (9x² + 25y²)(9x² - 25y²)
To simplify the answer, we can further factor the difference of squares 9x² - 25y² as (3x + 5y)(3x - 5y), which gives us the completely factored expression:
81xâ´ - 625yâ´ = (9x² + 25y²)(3x + 5y)(3x - 5y)
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Answer:
The expression is a difference of squares, and can be factored out completely using the formula [tex](a+b)(a-b)=a^2-b^2[/tex]
Notice that
[tex]9^2=81\\25^2=625\\[/tex]
and [tex](x^2)^2=x^4[/tex] because [tex](a^x)(a^y) =a^x^+^y[/tex] by the product rule of exponents
[tex]81x^4 - 625y^4\\[/tex]
Using the product property, we can simply this expression into
[tex](9)^2(x^2)^2 - (25)^2(y^2)^2[/tex]
Therefore, the factored form is
[tex](9x^2+25y^2)(9x^2-25y^2)[/tex]
