Name: Factorisation Using Difference of Two Squares
Uploaded: 2019-07-19
Duration: 5 min 14 s
Description: Sometimes writing a polynomial as the difference of two squares is the only way to factorise it. So let’s learn how to do it in this simple video!

Question

Mark four numbers forming a square in a calendar:

4	5
11	12

Add the squares of the diagonal pair and find the difference of these sums:

4^{2} + 12^{2} = 160

$11^{2} + 5^{2} = 146$

$160 - 146 = 14$

Explain using algebra, why the difference is $14$ always.

Accepted Answer

Given, four numbers forming a square in a calendar:

4 5

11 12

When we add the squares of the diagonal pair and find the difference of these sums we always get $14$ as answer.
$4^{2} + 12^{2} = 160$
$11^{2} + 5^{2} = 146$

$160 - 146 = 14$

We have to explain why the difference is $14$ always using algebra.

For this we will take the first number in the square as $x$ ,

x x+1

x+7 x+8

Now, the squares of diagonal are:

$\Rightarrow x^{2}$ and $(x + 8)^{2}$

$\Rightarrow (x + 7)^{2}$ and $(x + 1)^{2}$

Add the squares of the diagonal pair

$\Rightarrow x^{2} + {(x + 8)}^{2} = x^{2} + (x^{2} + 8^{2} + 2 \times x \times 8)$

[Using identity $160 - 146 = 14$ ]

$\Rightarrow x^{2} + {(x + 8)}^{2} = 2 x^{2} + 64 + 16 x$

Add the squares of the other pair of diagonals

$\Rightarrow (x + 1)^{2} + (x + 7)^{2}$

$\Rightarrow (x^{2} + 1 + 2 \times x \times 1) + (x^{2} + 7^{2} + 2 \times x \times 7)$

$\Rightarrow (x^{2} + 1 + 2 x) + (x^{2} + 49 + 14 x)$

$\Rightarrow 2 x^{2} + 16 x + 50$

Now subtract the difference of the sums:

$\Rightarrow (2 x^{2} + 64 + 16 x) - (2 x^{2} + 16 x + 50)$

$\Rightarrow 2 x^{2} + 64 + 16 x - 2 x^{2} - 16 x - 50$

$\Rightarrow 64 - 50$

$\Rightarrow 14$

So we can state that the difference is $14$ always.

Hence, proved.

Mark four numbers forming a square in a calendar:

4 5

11 12

Add the squares of the diagonal pair and find the difference of these sums:
$4^{2} + 12^{2} = 160$
$11^{2} + 5^{2} = 146$

$160 - 146 = 14$

Explain using algebra, why the difference is $14$ always.

Important Questions on Identities

Learn and Prepare for any exam you want !

Mark four numbers forming a square in a calendar: 4 5 11 12 Add the squares of the diagonal pair and find the difference of these sums: 42+122=160 112+52=146 160-146=14 Explain using algebra, why the difference is 14 always.

Important Questions on Identities

Learn and Prepare for any exam you want !

Mark four numbers forming a square in a calendar:

4 5

11 12

Add the squares of the diagonal pair and find the difference of these sums:
$4^{2} + 12^{2} = 160$
$11^{2} + 5^{2} = 146$

$160 - 146 = 14$

Explain using algebra, why the difference is $14$ always.