CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

(a+b)(a-b) Expansion and Visualisation

Find the HCF ...

Question

Find the HCF of the following pair of polynomials:
$x^{2} - x y - 2 y^{2}$ and $x^{2} + 3 x y + 2 y^{2}$

Open in App

Solution

We know that $H C F$ is the highest common factor.

Factorise $x^{2} - x y - 2 y^{2}$ as follows:

$x^{2} - x y - 2 y^{2} = x^{2} - 2 x y + x y - 2 y^{2} = x (x - 2 y) + y (x - 2 y) = (x + y) (x - 2 y)$

Now, factorise $x^{2} + 3 x y + 2 y^{2}$ as follows:

$x^{2} + 3 x y + 2 y^{2} = x^{2} + 2 x y + x y + 2 y^{2} = x (x + 2 y) + y (x + 2 y) = (x + y) (x + 2 y)$

Since the common factor between the polynomials $x^{2} - x y - 2 y^{2}$ and $x^{2} + 3 x y + 2 y^{2}$ is $(x + y)$ .

Hence, the $H C F$ is $(x + y)$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find the HCF of the following pair of polynomials:

x^{2} - x y

x^{2} - y^{2}

Q. The pairs of straight lines

x^{2} - 3 x y + 2 y^{2} = 0

x^{2} - 3 x y + 2 y^{2} + x - 2 = 0

Q. Find the GCD of the following

x^{2} + 3 x y + 2 y^{2}, x^{2} + 5 x y + 6 y^{2}

Q. What is the HCF of

4 x^{3} + 3 x^{2} y - 9 x y^{2} + 2 y^{3}

x^{2} + x y - 2 y^{2}

?

Q. Find the HCF of the following pair of polynomials:

x^{2} - 2 x + 1

x^{2} - 3 x + 2

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

(a+b)(a-b) Expansion and Visualisation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

(a+b)(a-b) Expansion and Visualisation

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon