Find the HCF: 9x²-3y²-8yz-4z² 4z²-4y²-9x²-12xy and 9x²+12xz+4z²-4y². | HCF and LCM | SciPiPupil

Find the HCF: $9x^2-4y^2-8yz-4z^2, 4z^2-4y^2-9x^2-12xy, 9x^2+12xz+4z^2-4y^2$.

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,

$1^{st} expression = 9x^2-4y^2-8yz-4z^2$

= $9x^2- (4y^2+8yz+4z^2)$

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

= $(3x+2y+2z)(3x-2y-2z)$

$2^{nd} expression = 4z^2-4y^2-9x^2-12xy$

= $4z^2-(4y^2+12xy+9x^2)$

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

= $(3x+2y+2z)(2z-2y-3x)$

$3^{rd} expression = 9x^2+12xz+4z^2-4y^2$

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

= $(3x+2y+2z)(3x-2y+2z)$

Therefore, the HCF = $(3x+2y+2z)$

Explanation to the above answer.

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

Step 2: Take the '-' sign common and re-write the last three terms of the expression.

Step 3: Write the terms in the form of squares. As we took the minus sign common, we got an expanded formula of (a+b)² = (a²+2ab+b²) in the last three terms. So, we write expression in the form of (a+b)² instead.

Step 4:  We have the expression in the form of (a²-b²) so, we write in the form of (a+b)(a-b) instead. 

Step 5: Write the second expression given in the question.

Step 6: Take the '-' sign common and re-write the last three terms of the expression.

Step 7: Write the terms in the form of squares. As we took the minus sign common, we got an expanded formula of (a+b)² = (a²+2ab+b²) in the last three terms. So, we write expression in the form of (a+b)² instead.

Step 8:  We have the expression in the form of (a²-b²) so, we write in the form of (a+b)(a-b) instead. 

Step 9: Write the third expression given in the question.

Step 10: Write the terms in the form of squares. We have an expanded formula of (a+b)² = (a²+2ab+b²) in the first three terms. So, we write expression in the form of (a+b)² instead.

Step 11: We have the expression in the form of (a²-b²) so, we write in the form of (a+b)(a-b) instead. 

Step 12: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (3x+2y+2z) are the 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 HCF: 9x²-3y²-8yz-4z² 4z²-4y²-9x²-12xy and 9x²+12xz+4z²-4y². | HCF and LCM | SciPiPupil

#SciPiPupil

#HCF

#Algebra