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Multiply (1)/(2)a^(2)b-(2)/(3)ab^(2)+b b...

Multiply `(1)/(2)a^(2)b-(2)/(3)ab^(2)+b` by 6abc:

A

`3a^3b^2c-4a^2b^3c+30abc`

B

`3a^3b^3c-4a^3b^2c+6abc`

C

`6a^3b^2+18ab^2c+30abc`

D

none of these

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The correct Answer is:
A
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If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x+(1)/(x)=2, thenx^(2)+(1)/(x^(2)) is equal to

QUANTUM CAT-ELEMENTS OF ALGEBRA-QUESTION BANK
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  3. Multiply (1)/(2)a^(2)b-(2)/(3)ab^(2)+b by 6abc:

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  4. Find the product of ((1)/(2)x^(2)-(1)/(3)y^(2))and((1)/(2)x^(2)+(1)/(3...

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  5. Divide 36x^(2)y^(5)+42xy^(3)-24x^(3)y^(2)-12y^(5) by -6y^(2).

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  9. if (5x^2 + 14x + 2)^2 - (4x^2 - 5x + 7)^2 is divided by x^2 + x + 1, ...

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  11. When (x^4-3x^3+2x^2-5x+7) is divided by (x-1) then the remainder is

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  13. If (x^11+1) is divided by (x-1) then the remainder is

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  17. If (y-1) is a factor of (y^2+3qy-2q) then the value of q is:

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  19. Which one of the following is a factor of x^4-5x^3+5x^2-10x+24?

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  20. If (x+a) be a common factor of x^2 + px + q and x^2 + p'x +q', then th...

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