Find the HCF: x³-8y³ and x²+2xy+4y² | HCF and LCM | SciPiPupil

Find the HCF: $x^3-8y^3$ and $x^2+2xy+4y^2$.

This is a class 10 Question From H.C.F. chapter of Unit Algebra (Mathematics). All the steps for the solutions are mentioned in the description below. If that's hard for you to navigate, you can always visit the facebook link given at the end of every posts.

Solution:

Given,

$1^{st} expression = x^3-8y^3$

= $(x)3-(2y)^3$

= $(x-2y)(x^2 +2xy+4y^2)$

$2^{nd} expression = $(x^2+2xy+4y^2)$

Therefore, the HCF = $(x^2+2xy+4y^2)$

Explanation to the above answer.

Step 1: Write the first expression given in the question.

Step 2: Here, we are finding H.C.F. using factorisation. And, we can convert this expression into a³-b³. So, let's do this.

Step 3:  Expand the expression as (a³-b³) = (a-b)(a²+ab+b²).

Step 4: Write the second expression given in the question.

Step 5: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (x²+2xy+4y²) are the common factors.

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Question: Find the HCF: x³-8y³ and x²+2xy+4y² | HCF and LCM | SciPiPupil

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