Question & Answer
QUESTION

Solve 88 × 112 by using formula.

ANSWER Verified Verified
Hint: Do not directly multiply 88 and 112. We need to solve it by using the formula. Write 88 and 112 in terms of 100 and then use the formula \[{a^2} - {b^2} = (a - b)(a + b)\] to evaluate the expression.

Complete step-by-step answer:
We need to multiply 88 and 112 by using formula.
We know that 88 and 112 can be written in terms of 100.
The number 88 is 100 – 12 and the number 112 is 100 + 12.
Then, we have the following:
88 × 112 = (100 – 12)( 100 + 12)………….(1)
Now, it is of the form \[(a - b)(a + b)\]. We can evaluate it using the formula. First let us derive the formula for your understanding.
Multiplying the terms inside the bracket, we get the following:
\[(a - b)(a + b) = a.a + a.b - a.b - b.b\]
Simplifying and cancelling the common terms, we have:
\[(a - b)(a + b) = {a^2} - {b^2}..........(2)\]
Comparing formula (2) and the equation (1), we have a = 100 and b = 12.
Using the formula (2) in equation (1) to evaluate the expression, we have:
\[88 \times 112 = {100^2} - {12^2}\]
We know that the square of 100 is 10000 and the square of 12 is 144. Hence, we get as follows:
\[88 \times 112 = 10000 - 144\]
Simplifying the above expression, we have:
\[88 \times 112 = 9856\]
Hence, the value of 88 × 112 is 9856.

Note: You are asked to multiply 88 and 112 using formula, hence, if you directly evaluate the expression using the multiplication method, your solution will be considered wrong. However, you can verify the final answer by solving the above using direct multiplication.