Factor each polynomial. 27y^{9}+125z^{6}

Josh Sizemore

Josh Sizemore

Answered question

2021-12-15

Factor each polynomial.
27y9+125z6

Answer & Explanation

Ana Robertson

Ana Robertson

Beginner2021-12-16Added 26 answers

Step 1
We try to write the polynomial as the sum of two cubes.
For that, we use 27=33 and 125=53
27y9+125z6
=(3y3)3+(5z2)3
Step 2
Then we use the sum of two cubes formula
a3+b3=(a+b)(a2ab+b2)
With a=3y3 and b=5z2
(3y3)3+(5z2)3
=(3y3+5z2)[(3y3)2(3y3)(5z2)+(5z2)2]
=(3y3+5z2)(9y615y3z2+25z4)
Answer: (3y3+5z2)(9y615y3z2+25z4)
vrangett

vrangett

Beginner2021-12-17Added 36 answers

Step 1
We have to factorize the polynomial:
27y9+125z6
Rewriting the polynomial,
27y9+125z6=(3y3)3+(5z2)3
We know the formula for sum of two cubes,
a3+b3=(a+b)(a2ab+b2)
Step 2
Applying above formula,
(3y3)3+(5z2)3=(3y3+5z2)((3y3)2(3y3)(5z2)+(5z2)2)
=(3y3+5z2)(9y615y3z2+25z4)
Hence, factorized form of the polynomial is (3y3+5z2)(9y615y3z2+25z4).

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