Question

Find the GCD a³-9ax²,(a-3x)²

Answer 1

Answer:

(a-3x)

Step-by-step explanation:

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Answer 2

Answer:

(a- 3x ) is the required GCD of the given polynomials .

Step-by-step explanation:

Explanation :

Given , ($a^{3} - 9ax^{2}$) , $(a-3x)^{2}$

GCD stand for Greatest Common Divisor  of a set numbers is the largest number that divides all the numbers in the set without remainder .

We have  ($a^{3} - 9ax^{2}$) , $(a-3x)^{2}$ ,

Now , applying factorization method  we get ,

$a^{3} -9ax^{2}$ = a($a^{2} - 9x^{2}$)           (taking  common "a" )

As , we know that $a^{2} - b^{2} = (a +b )(a -b)$ ,

⇒$a^{3} -9ax^{2}$ = a($a^{2} - 9x^{2}$)   = a[$a^{2} - (3x^{2} )$]

= a(a+ 3x)(a- 3x).

Now ,  $(a-3x)^{2}$ =  (a -3x)(a-3x)

Here we can see that (a - 3x ) is common from both the given polynomial

Final answer:

Hence , GCD of ($a^{3} - 9ax^{2}$) , $(a-3x)^{2}$ is (a-3x) .

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