Find the H.C.F. of (x²-y²) and (x²+2xy+y²). | H.C.F. | SciPiPupil

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

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,

$1^{st}\; expression\;=\;x^2-y^2$

= $(x+y)(x-y)$

$2^{nd}\; expression\;=\;x^2+2xy+y^2$

= $(x+y)²$

= $(x+y)(x+y)$

Therefore, The H.C.F. = (x+y)

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. So, find the factors of the first expression. We find the factors using the formula (a²-b²) = (a+b)(a-b).

Step 3: Write the second expression given in the question.

Step 4: This expression is an expanded form of (a+b)² = (a²+2ab+b²). So, we write it in square form. 

Step 5: To make it easy to find HCF, we write (x+y)² in factor form.

Step 6: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (x+2) are the only common factors.

Here is the Facebook link to the solution of this question in image. 

Here is the Website link to the guide of solving HCF and LCM.

Question: Find the H.C.F. of (x²-y²) and (x²+2xy+y²). | H.C.F. | SciPiPupil

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