Advertisements
Advertisements
Question
Evaluate the following product without multiplying directly:
95 × 96
Advertisements
Solution
95 × 96 = (100 − 5) (100 − 4)
= (100)2 + (− 5 − 4) 100 + (− 5) (− 4)
By using the identity (x + a)(x + b) = x2 + (a + b)x + ab,
where, x = 100, a = −5 and b = −4
= 10000 − 900 + 20
= 9120
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
If `x + 1/x = sqrt5`, find the value of `x^2 + 1/x^2` and `x^4 + 1/x^4`
Write in the expanded form (a2 + b2 + c2 )2
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]
Use identities to evaluate : (97)2
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
(xy+4) (xy−4)
Expand the following:
`(2"a" + 1/(2"a"))^2`
If m - n = 0.9 and mn = 0.36, find:
m + n
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
Simplify:
(7a +5b)2 - (7a - 5b)2
Find the following product:
(x2 – 1)(x4 + x2 + 1)
