FACTORISE 1. 27-125a³-135a+225a²2. 64a³-27b³-144a²b+108 ab²2 ❌DON’T SPAM ❌CLASS 9 MATHS CHAPTER 2 POLYNOMIALS About the author Savannah
Answer: 27-125a³-135a+225a = (3-5a)³ = (3-5a)(3-5a)(3-5a) Given 27-125a³-135a+225a =3³+(-5a)³+3×3²×(-5a)+3×3×(-5a)² = [3+(-5a)]³ By an algebraic identity: [tex]\boxed {x^{3}+y^{3}+3x^{2}y+3xy^{2}\\=(x+y)^{3}} */[/tex] =(3-5a)³ Therefore, 27-125a³-135a+225a = (3-5a)³ Step-by-step explanation: Plz mark as brainliest..! Reply
Step-by-step explanation: Given :– 1. 27-125a^3-135a+225a^2 2. 64a^3-27b^3-144a^2b+108 ab^2 To find:– Factorise the following expressions ? Solution:– 1) Given expression is 27-125a^3-135a+225a^2 It can be written as =>(3)^3-5^3a^3-3(9)(5a)+3(3)(25)a^2 => (3)^3-5^3a^3-3(3^2)(5a)+3(3)(5a)^2 => (3)^3-3(3^2)(5a)+3(3)(5a)^2-(5a)^3 This is in the form of a^3-3a^2b+3ab^2-b^3 Where a = 3 and b = 5a We know that (a-b)^3 = a^3-3a^2b+3ab^2-b^3 => (3)^3-3(3^2)(5a)+3(3)(5a)^2-(5a)^3 => (3-5a)^3 => (3-5a)(3-5a)(3-5a) 27-125a^3-135a+225a^2 = (3-5a)(3-5a)(3-5a) —————————————————————- 2) Given expression is 64a^3-27b^3-144a^2b+108 ab^2 It can be written as =>4^3a^3-3^3b^3-3(16a^2)(3b)+3(4a)(9b^2) =>( 4a)^3-(3b)^3-3(4a)^2(3b)+3(4a)(3b)^2 => ( 4a)^3-3(4a)^2(3b)+3(4a)(3b)^2-(3b)^3 This is in the form of a^3-3a^2b+3ab^2-b^3 Where a = 4a and b = 3b We know that (a-b)^3 = a^3-3a^2b+3ab^2-b^3 =>( 4a)^3-3(4a)^2(3b)+3(4a)(3b)^2-(3b)^3 => (4a-3b)^3 => (4a-3b)(4a-3b)(4a-3b) 64a^3-27b^3-144a^2b+108 ab^2 = (4a-3b)(4a-3b)(4a-3b) –––––———————————————————– Used Identity:– (a-b)^3 = a^3-3a^2b+3ab^2-b^3 Reply
Answer:
27-125a³-135a+225a
= (3-5a)³
= (3-5a)(3-5a)(3-5a)
Given 27-125a³-135a+225a
=3³+(-5a)³+3×3²×(-5a)+3×3×(-5a)²
= [3+(-5a)]³
By an algebraic identity:
[tex]\boxed {x^{3}+y^{3}+3x^{2}y+3xy^{2}\\=(x+y)^{3}} */[/tex]
=(3-5a)³
Therefore,
27-125a³-135a+225a = (3-5a)³
Step-by-step explanation:
Plz mark as brainliest..!
Step-by-step explanation:
Given :–
1. 27-125a^3-135a+225a^2
2. 64a^3-27b^3-144a^2b+108 ab^2
To find:–
Factorise the following expressions ?
Solution:–
1)
Given expression is 27-125a^3-135a+225a^2
It can be written as
=>(3)^3-5^3a^3-3(9)(5a)+3(3)(25)a^2
=> (3)^3-5^3a^3-3(3^2)(5a)+3(3)(5a)^2
=> (3)^3-3(3^2)(5a)+3(3)(5a)^2-(5a)^3
This is in the form of a^3-3a^2b+3ab^2-b^3
Where a = 3 and b = 5a
We know that
(a-b)^3 = a^3-3a^2b+3ab^2-b^3
=> (3)^3-3(3^2)(5a)+3(3)(5a)^2-(5a)^3
=> (3-5a)^3
=> (3-5a)(3-5a)(3-5a)
27-125a^3-135a+225a^2
= (3-5a)(3-5a)(3-5a)
—————————————————————-
2)
Given expression is 64a^3-27b^3-144a^2b+108 ab^2
It can be written as
=>4^3a^3-3^3b^3-3(16a^2)(3b)+3(4a)(9b^2)
=>( 4a)^3-(3b)^3-3(4a)^2(3b)+3(4a)(3b)^2
=> ( 4a)^3-3(4a)^2(3b)+3(4a)(3b)^2-(3b)^3
This is in the form of a^3-3a^2b+3ab^2-b^3
Where a = 4a and b = 3b
We know that
(a-b)^3 = a^3-3a^2b+3ab^2-b^3
=>( 4a)^3-3(4a)^2(3b)+3(4a)(3b)^2-(3b)^3
=> (4a-3b)^3
=> (4a-3b)(4a-3b)(4a-3b)
64a^3-27b^3-144a^2b+108 ab^2 = (4a-3b)(4a-3b)(4a-3b)
–––––———————————————————–
Used Identity:–