Question

Fill in the blanks to calculate using suitable identities.

a) 105²

= (100 +
)²

= (
)² + 2 X
X 5 + (
)²

=
+
+
=
b) 97²

= (
-
)²

= (
)² ─ 2 X
X
+ (
)²

= 10000 ─
+
=
c) 108 x 92

= (100 +
) x (
─
)

=
² ─
²

=
─
=
d) 103 x 104

= (100 +
) x (
+
)

= (
)² + 100 (
+
) + (
x
)

=
+
+
=
e) 12.2² ─ 7.8²

= (12.2 +
) x (
─
)

=
X
=
f) 96 x 103 =

(100
)(100 +
)

= (
)² + 100 (
+
) + (
x
)

=
─
─
=

Answer 1

Answer:

:

(i) 712=(70+1)2

(70)2+2(70)(1)+(1)2

=4900+140+1=5041

(ii) 992=(100−1)2

=1002−2(100)(1)+1

=10000−200+1

=9801

(iii) 1022=(100+2)2

=1002+22+2⋅2⋅100=200+4+400=604

(iv) 9982=(100−2)2

=1002+22−2⋅2⋅100=−200+4=−196

(v) 5.22=(5+0.2)2

=52+0.22+2(0.2)(5)

=25+0.04+2=27.04

(vi) 297×303=(300−3)×(300+3)

=(300)2−32

=90000−9=89991

(vii)78×82=(80−2)(80+2)

(80)2−(2)2=6400−4=6396

(viii) 8.92=(9−0.1)2

=92+0.12−2(0.1)(9)

=81+0.01−1.8

=79.21

(ix) 1.05×9.5

105100×95100

=(100+5)(100−5)1000

=1002−521000

=10000−251000

=99751000=9.975

Answer 2

Answer:

i have reported ur questions