Question

Find the value of $1.05 \times 0.95$ using standard identity.
A) 0.9985
B) 0.9975
C) 0.9875
D) 0.9995

Answer 1

Hint:
Here we need to find the value of the given mathematical expression. We will first write the first number as the sum of two numbers and the second number as the difference of two numbers. Then we will apply the algebraic identity in the mathematical expression and we will then further simplify it to get the final value of the required mathematical expression.

Complete step by step solution:
Here we need to find the value of the given mathematical expression.
The given mathematical expression is $1.05 \times 0.95$
For that, we will first write the first number as the sum of two numbers and the second number as the difference of two numbers.
We can write 1.05 as the sum of the numbers 1 and 0.05 i.e. $1.05 = 1 + 0.05$ and we can write 0.95 as difference of the numbers 1 and 0.05 i.e. $0.95 = 1 - 0.05$.
Now, we will substitute these values in the given expression.
$ \Rightarrow 1.05 \times 0.95 = \left( {1 + 0.05} \right)\left( {1 - 0.05} \right)$
We know the algebraic identity that $\left( {a - b} \right)\left( {a - b} \right) - {a^2} - {b^2}$.
Now, we will use the same algebraic identity here.
$ \Rightarrow 1.05 \times 0.95 = {1^2} - {\left( {0.05} \right)^2}$
Now, we will find the square of the numbers.
$ \Rightarrow 1.05 \times 0.95 = 1 - 0.0025$
Now, we will subtract these numbers.
$ \Rightarrow 1.05 \times 0.95 = 0.9975$.

Hence, the correct option is option B.

Note:
Here we have obtained the value of the mathematical expression using the algebraic identity. Here algebraic identities are defined as the equalities which are true for all values of the variable. The algebraic identities are mostly used for the factorization of polynomials i.e. the algebraic identities are used for computation of different mathematical expressions and for solving different polynomials to make it easier and shorter.