Page 54 - SM inner class 8.cdr

Example 24. Find the square of 5x + 3y \ (x + 3a) (x + 7 ) a
2
7
2
)
(
(
Solution: (5x + 3y ) = (5x ) 2 + . .3y + (3y ) = x 2 + 3 a + a x + 3 a) (7a )
x
2
5
(Using Identity 1) ( Using Identity 4)
= 25x 2 + 30xy + 9y 2 = x 2 + 10 ax + 21 a 2
2
2
Example 25. Find the square of 9a - b Example 31. Multiply 3a - 7 by 3a - 9.
2
2
Solution: (9a - ) b 2 = ( )9a 2 - . . b + b 2 Solution: (3a - 7 ) (3a - ) 9
9
a
2
)
7
9
(
(Using Identity 2) = (3a 2 2 + - - ) 3a 2 + (-7 ) (-9 )
= 81a 2 -18ab + b 2 ( Using Identity 4)
Example 26. Find the square of 999 = 9a 4 - 48a 2 + 63
Solution: 999 = 1000 - 1 Example 32. If x + y =12 and xy =14 find the
2
2
2
1
(999 ) = (1000 - ) 2 value of x + y
(Using Identity 2) Solution: x + y =12
= (1000 ) 2 - 21000 xy =14; x 2 + y 2 = ?
2
2
1 + ( 1) 2 using the identity (a + ) b = a 2 + b 2 + ab
2
=1000000 - 2000 + 1 (x + ) y 2 = x 2 + y 2 + xy
2
(
= 998001 (12 ) = x 2 + y 2 + 2 14)
144 = x 2 + y 2 + 28
Example 27. Using an appropriate formula to
multiply 2x + 3 by 2x - 3. 144-28 = x 2 + y 2
2
2
Solution: (2x + 3 ) (2x - ) 3 \ x + y =116
3
= (2x ) 2 - ( ) 2 Example 33. Find:
(Using Identity 3) a. ç æ 3 x + 2 ö æ 3 x - 2 ö
y÷ ç
y÷
= 4x 2 - 9 è 2 3 ø è 2 3 ø
Example 28. Find 407 ´ 393 æ 3 2 ö æ 3 2 ö
Solution: a. ç x + y÷ ç x - y÷
)
(
Solution: 407 ´ 393 = ( 400 + 7 400 - 7) è 2 3 ø è 2 3 ø
= 400 2 - 7 2 æ3 ö 2 æ2 ö 2
= ç x ÷ - ç y ÷
( Using Identity 3) è 2 ø è 3 ø
= 160000 – 49 9 4
= x 2 - y 2
= 159951 4 9
2
Example 29. Find 987 - 13 2 Example 34. Find the value of the expression
2
2
2
2
Solution: 987 - 13 = (987 + 13)(987 – 13) (16x + 9y - 24xy ) when x = 5 and y = -5.
2
2
( Using Identity 3) Solution: We have 16x + 9y - 24xy
2
= 1000 ´ 974 = 974000 = (4x ) 2 + (3y ) 2 - (4x )(3y )
Example 30. Multiply x + 3 a by x + 7 a = (4x - 3y ) 2
2
Now (4x - 3y ) at x = 5, y = -5
Solution: The first term of both the 2 2
4
-
5
(
-
expressions is x & the second terms are 3a and [ ( ) 3 5 )] = (20 + 15 )
7a respectively. = (35 ) 2 =1225
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Mathematics In Focus - 8