Find the following using the identitya 160 - 94b 0-99 - 1-01

You visited us 7 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

(x±a)(x±b) = x²±(a+b)x+ab.

Find the foll...

Question

Find the following using the identity
a) $160 \times 94$
b) $0.99 \times 1.01$

Open in App

Solution

$106 \times 94 = (100 + 6) (100 - 6)$
Now, we know $(a + b) (a - b) = a^{2} - b^{2}$
So, $(100 + 6) (100 - 6) = 100^{2} - 6^{2}$
$= 10000 - 36$
$= 9964$

b. $(998)^{2} = (1000 - 2)^{2}$
$1000^{2} + 2^{2} - 2 \times 2 \times 1000 [∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b]$
$1000 \times 1000 + 4 - 4 \times 1000$
$996000 + 4$
$996004$

Suggest Corrections

Similar questions

Q. Fill in the blanks by using > or < to complete the following:

0.93 . . . 0.99

Q. Find an approximation of

(0.99)^{5}

using the first three of its expansion.

Find the mean of the following data, using assumed-mean method:
$\begin{matrix} Marks & 100 - 120 & 120 - 140 & 140 - 160 & 160 - 180 & 180 - 200 Number of students & 10 & 20 & 30 & 15 & 5 \end{matrix}$

Find an approximation of (0.99)⁵ using the first three terms of its expansion.

Q. Find an approximation of (0.99) 5 using the first three terms of its expansion.

Join BYJU'S Learning Program

Find the following using the identity a) 160×94 b) 0.99×1.01

106×94=(100+6)(100−6) Now, we know (a+b)(a−b)=a2−b2 So, (100+6)(100−6)=1002−62 =10000−36 =9964 b. (998)2=(1000−2)2 10002+22−2×2×1000 [∵(a−b)2=a2+b2−2ab] 1000×1000+4−4×1000 996000+4 996004

Find the following using the identity
a) $160 \times 94$
b) $0.99 \times 1.01$