Factorise the question 27y^3+125z^3
Answers
Answer:
Factorization of 27 y^{3}+125 z^{3}\ \text{is}\ \bold{(3 y+5 z)\left(9 y^{2}+25 z^{2}-15 y z\right)}y
3
+125z
3
is (3y+5z)(9y
2
+25z
2
−15yz)
Given:
27 y^{3}+125 z^{3}27y
3
+125z
3
To find:
Factorization of 27 y^{3}+125 z^{3}27y
3
+125z
3
Solution:
We have to factorize -
27 y^{3}+125 z^{3}=(3 y)^{3}+(5 z)^{3} \rightarrow(1)27y
3
+125z
3
=(3y)
3
+(5z)
3
→(1) [ Since 27 = cube of 3, 125 = cube of 5]
We know that a^{3}+b^{3}=(a+b)\left(a^{2}+b^{2}-a b\right)a
3
+b
3
=(a+b)(a
2
+b
2
−ab)
Let, a = 3y, b= 5z
Hence,
(3 y)^{3}+(5 z)^{3}=(3 y+5 z)\left[(3 y)^{2}+(5 z)^{2}-(3 y)(5 z)\right](3y)
3
+(5z)
3
=(3y+5z)[(3y)
2
+(5z)
2
−(3y)(5z)]
(3 y)^{3}+(5 z)^{3}=(3 y+5 z)\left(9 y^{2}+25 z^{2}-15 y z\right) \rightarrow(2)(3y)
3
+(5z)
3
=(3y+5z)(9y
2
+25z
2
−15yz)→(2)
From eq. (1) and (2) we get,
27 y^{3}+125 z^{3} \equiv(3 y+5 z)\left(9 y^{2}+25 z^{2}-15 y z\right)27y
3
+125z
3
≡(3y+5z)(9y
2
+25z
2
−15yz)
Step-by-step explanation:
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Step-by-step explanation:
(3y)^3+(5z)^3
using formula
a^3+b^3=(a+b )(a^2+b^2-ab)
(3y+5z)(9y^2+25z^2-15yz)