Question

The hcf of 14 x cube y square and 21 y cube z square is. 7y square is the answer explain the steps.​ if you tell the correct steps i will mark as brainilist or else i will report u. pls tell me the correct steps all are telling 7y 7y. it is not 7y it is 7y square​

Answer 1

It's not a big problem I guess. Leaving aside the answer you are telling, let us first understand what we mean by HCF of algebraic expression and then we will solve the problem.

As we know, HCF is highest common factor. This is the biggest number that divides the given numbers completely.

We derive HCF of numbers by long division method or prime factorisation method.

The factorisation method goes well to find HCF of algebraic expression

In algebraic expression, we represent each term as multiplication of

1. prime factors of numbers

2, each variable with its exponent

then we choose

1. such number factors as are present in all algebraic expressions

2. such variables which are present in all algebraic expressions. we choose variable with least exponent.

thus we find HCF..now we try solving our problem

the expressions are

14 x^3 y^2

21 y^3 z^2

factorisation of

14 x^3 y^2 = 2*7 x^3 y^2. (it's already done)

21 y^3 z^2 = 3*7 y^3 z^2

clearly,

7 is present in both expressions, 2 is not present in second and 3 is not present in the first expression.

so our number is 7

variable x is present in the first expressions but not in second expression. so we will leave it

variable y is present in both expressions. it has exponent 2 in the first expression and 3 in the second expression. the least is 2. so our letter is y^2.

z is not present in the first expression, so we will leave it.

so HCF = our selected number and letters

= 7y^2

yes, you were right!!!!