Page 55 - SM inner class 8.cdr

E xercise 6.4

Solve using Iden ti ties:
b
,
1. 4x + 3 4x - 3 2. 5a + 8 5a - 8b 3. 4a + 7 4a - 7b 4. 13 12 13 12- p, + p
,
b
,
2
2
2
2
5. ax + b ax - b 6. a b c a b C- - , + + 7. x - x 1, x + x 1
+
,
+
4
2
2
2
2
8. a + 3 a x + x 9 2 + x 9 4 - 3 a x + a 4 9. x +16, x + 9 10. Px + 3, Px -5
2 1
2
2
2
2
11. 2x + 5 2x + 8 12. q x + r q x + r 3 13. x + , x +
,
,
3 3
14. Evaluate the following by using suitable identities:
(i) (304 ) 2 (ii) (509 ) 2 (iii) (992 ) 2 (iv) (799 ) 2
4 æ 5 ö æ 4 5 ö
(v) 304 296´ (vi) 83 77´ (vii) ç x + y÷ ç x - y÷
5 è 4 ø è 5 4 ø
2
2
15. Evaluate 196x - 56xy + 4y if x =1, y =2.
Summary
m There are number of situations in which we need to multiply algebraic expressions.
m A monomial multiplied by a monomial always gives a monomial.
m While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the monomial.
m In carrying out the multiplication of an algebraic expression with another algebraic expression (monomial /
binomial / trinomial etc.) we multiply term by term i.e. every term of the expression is multiplied by every
term in the another expression.
m We can divide a polynomial by a binomial using factor method or long division method.
m An identity is an equation, which is true for all values of the variables in the equation. On the other hand, an
equation is true only for certain values of its variables. An equation is not an identity.
m The following are identities:
2
2
2
2
+
I. (a b+ ) = a + 2 ab b 2 II. (a b- ) = a -2 ab b 2
+
2
2
+
III. (a b+ )(a b ) a - b 2 IV. (x + a )(x + ) b = x + (a b x + ab
-
)
=
m The above four identities are useful in carrying out squares and products of algebraic expressions. They
also allow easy alternative methods to calculate products of numbers and so on.
Review Exercise
1. Find the prod uct of the follow ing pairs:
2
(i) 6 7, k (ii) -3l, -2m (iii) -5t , 3t 2
2. Find the prod uct of (-4xy )(2x - ) y
(
,
-
3. Add the prod uct: x x( + y r),( - y r z x - y z)
x
-
+
)
4. Subtract 3k(5k - l + 3m) from 6k (2k + 3l - 2m)
5. Find 96 104´ using alge braic iden tity.
6. Select a suit able iden tity and find the follow ing prod ucts
2
2
(i) (3k + 4l )(3k + ) 4 (ii) (ax + by 2 )(ax + by 2 )
2
2
(iii) (7d - 9e )(7d - 9e ) (iv) (m - n 2 )(m + n 2 )
2
7. Find 285 - 15 2
2
8. If 3x - 5y = 10 and xy =5, then find the value of 9x + 25y 2
2
9. 6x - 31x + 49 by 2x - 5 and verify that
Divi dend = Divi sor ´ Quotient + Remain der
2
4
3
+
10. Divide (4x - 2x + x + 10 10x - 25 ) by (x + 5 )
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Mathematics In Focus - 8