8

^{th}Algebraic IdentityQ. 1. Find products using suitable algebraic Identity

(i) ( x – 2/3 ) ( x+ 1/2 )

(ii) (x + 1/x ) ( x

^{4}+ 1/x^{4})(iii) ( -3 x + 8 ) ( 2 + 7 x )

(iv) 87 x 92

(v) 234 x 229

Q. 2. Expand each of the following

(i) (3/2xy – 5/4 y

^{2 }z – xyz)^{2}(ii) [ ( 2a-3b)

^{2 }]^{2 }(iii) (x

^{2}y – 2xy^{2}+5yz^{2})^{2}^{}(iv) [ (2m

^{2}/n - 3/r^{2 })^{2}]^{2}(v) [(2a-3b)

^{2}]^{2}Q. 3. Simplify

(i) (a + b + c)

^{2}+ (a - b + c)^{2 }(ii) (a - b - c)^{2}- (a + b - c)^{2 }^{}(iii) (1/2 l – 2/3 m - 1/5n)

^{2 }- ( 1/2 l +2/3 m -1/5n)

^{2}

Q.4. If a - b – c = 4 and –a b + b c – c a = -3 Find a

^{2}+ b^{2 }+ c^{2 }Q.5. If a

^{2}+ b^{2 }+ c^{2 }= 9 and b c+ ca + a b = 8 find ( a + b + c )^{2}Q6. x + y + z = 2 and x y + y z + z x = 1 find (x +y)

^{2}+ ( y + z )^{2}+ ( z + x )^{2}Q. 7. Expand

(i) ( - 4p +5q)

^{3 }^{ }(ii) ( - 2 l – 3 m )

^{3}

Q. 8. Find value (i) 8x

^{3 }+^{ }125 y^{3}If 2x + 5y = 7 and xy = 9Q. 9. If 3p – 5q = 4 and 27 p

^{3 }-125 q^{3 }= 8 Find pqQ. 10. If ( a + 1/a )

^{2 }= 3 Prove a^{3}+ 1/a^{3}= 0Q.11. ( x + 2) + = 5 find ( x + 2)

^{3}+Q.12. x + 1/x = P show x

^{3 }+ 1/x^{3}= p^{3 – }3p^{3 }^{}Q.13. y + 1/y = √3 prove y

^{3}+ 1/y

^{3}=0

Q. 14.(a2 +1)/a = 4 Show (a6+1)/a3 = 52

Q.15. If p = 12 , q= 3 Find Value of p

^{3}– 12p^{2}q + 48pq^{2}– 64 q^{3}**Algebraic Identity**

(a + b)

^{2 }= a^{2}+ b^{2}+2ab(a – b )

^{2 }= a^{2}+ b^{2}-2ab(x + a) (x + b) = x

^{2 }+( a + b) x +a b(a + b + c)

^{2 }= a^{2 }+ b^{2}+ c^{2}+ 2ab + 2bc + 2ca( a + b)

^{3 }= a^{3}+ b^{3}+3 a^{2 }b +3 a b^{2}= a^{3}+ b^{3}+3 a b (a + b)( a - b)

^{3}= a^{3}- b^{3}- 3 a^{2}b +3 a b^{2}= a^{3}+ b^{3}-3 a b (a - b)
one more identity is missing.......(a+b)(a-b)= a2- b2

ReplyDeletesrry i was not able to put the a and b square properly

Some of them are too tough.

ReplyDelete