Question

Using the identities for difference of two squares, find the product of 51 X 49.

Answer 1

Given:

Using the identities for the difference of two squares

To Find:

find the product of 51 X 49.

Solution:

Algebraic identities are the equations in which every value of variables of an algebraic equation is valid. There are many algebraic identities that help in the calculation of the algebraic equation.

The identity mentioned in the question is,

$a^2-b^2=(a-b)(a+b)$

So now we are given with,

$=51*49$

which can be expressed as required by the identity in, (50+1)(50-1), so we have,

[tex]=51*49\\ =(50+1)(50-1)\\ [/tex]

Now using the stated identity value we have,

[tex]=(50+1)(50-1)\\ =(50^2-1^2)\\ =2500-1\\ =2499[/tex]

Hence, the value of 51*49 is 2499.