Find the HCF: (4x³+8x²) and (5x³-20x) | HCF and LCM | SciPiPupil

Find the HCF: $4x^3+8x^2$ and $5x^3-20x$.

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,

$1^{st} expression = 4x^3+8x^2$

= $4x^2(x +2)$

= $4.x.x.(x+2)$

$2^{nd} expression = 5x^3-20x$

= $5x(x^2-4)$

= $5x(x^2-2^2)$

= $5x(x+2)(x-2)$

Therefore, HCF = $x(x+2)$

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. So, find the factors of the first expression. Taking 4x² as the common factor, we re-write the expression.

Step 3: For our easiness, we write everything in the expression in factor form. 

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

Step 5: Taking 5x as the common factor, we re-write the expression.

Step 6: To be able to further factorize this expression, we change the (x²-4) into (a²-b²).

Step 7: We expand (x²-2²) using the formula of (a²-b²) = (a+b)(a-b).

Step 8: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, x(x+2) are the only common factors.

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Question: Find the HCF: (4x³+8x²) and (5x³-20x) | HCF and LCM | SciPiPupil

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