Advertisements
Advertisements
Question
Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 95 × 105
Advertisements
Solution
Here, we will use the identity \[(a - b)(a + b) = a^2 - b^2\]
Let us consider the following product: \[95 \times 105\]
\[\because \frac{95 + 105}{2} = \frac{200}{2} = 100\];therefore, we will write the above product as:
\[95 \times 105\]
\[ = \left( 100 + 5 \right)\left( 100 - 5 \right)\]
\[ = \left( 100 \right)^2 - \left( 5 \right)^2 \]
\[ = 10000 - 25\]
\[ = 9975\]
Thus, the answer is 9975.
RELATED QUESTIONS
Show that (a - b)(a + b) + (b - c) (b + c) + (c - a) (c + a) = 0
Simplify the following using the formula: (a − b)(a + b) = a2 − b2: (79)2 − (69)2
If 2x + 3y = 14 and 2x − 3y = 2, find the value of xy.
[Hint: Use (2x + 3y)2 − (2x − 3y)2 = 24xy]
Find the following product: \[\left( y^2 + \frac{5}{7} \right)\left( y^2 - \frac{14}{5} \right)\]
Find the following product: (p2 + 16) \[\left( p^2 - \frac{1}{4} \right)\]
Expand the following:
(2p + 3) (2p – 4) (2p – 5)
On dividing p(4p2 – 16) by 4p(p – 2), we get ______.
Simplify:
`(7/9 a + 9/7 b)^2 - ab`
Simplify:
(a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab)
Expand the following, using suitable identities.
(a2 + b2)2
