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Multiply : 3a b^2c^3b y\ 5a^3b^2c (ii)...

Multiply : `3a b^2c^3b y\ 5a^3b^2c` (ii) `4x^2y z\ b y-3/2x^2y z^2`

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(i) `3a b^2c^3xx5a^3b^2c`
`15(axxa^3)(b^2xxb^2)(c^3xxc)`
`15a^4b^4c^4`
(ii) `4x^2yzxx-3/2x^2y z^2`
`4xx(-3/2)xx(x^2xx x^2)(yxxy)(zxxz^2)`
`-6x^2+2y^1+1z^1+2`
`-6x^4y^2z^3`
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Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

2x + 3y + 3z = 5, x-2y + z = -4,3x-y-2z = 3

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Subtract: (i) 5a + 7b - 2c from 3a - 7b + 4c (ii) a - 2b - 3c from -2a + 5b - 4c (iii) 5x^(2) - 3xy + y^(2) from 7x^(2) - 2xy - 4y^(2) (iv) 6x^(3) - 7x^(2) + 5x - 3 from 4 - 5x + 6x^(2) - 8x^(3) (v) x^(3) + 2x^(2) y + 6xy^(2) - y^(3) from y^(3) - 3xy^(2) - 4x^(2) (vi) -11 x^(2) y^(2) + 7xy - 6 from 9x^(2) y^(2) - 6xy + 9 (vii) -2a + b + 6d from 5a - 2b - 3c

By using properties of determinants. Show that: (i) |a-b-c2a2a2bb-c-a2b2c2cc-a-b|=(a+b+c)^3 (ii) |x+y+2z x y z y+z+2x y z x z+x+2y|=2(x+y+z)^3

Eliminate x, y, zx + y + z = 0x ^ (2) + y ^ (2) + z ^ (2) = a ^ (2) x ^ (3) + y ^ (3) + z ^ (3 ) = b ^ (3) x ^ (5) + y ^ (5) + z ^ (5) = c ^ (5)

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x

Factorize each of the following expressions: 2p(a-b)+3q(5a-5b)+4r(2b-2a)ab(a^(2)+b^(2)-c^(2))+bc(a^(2)+b^(2)-c^(2))-ca(a^(2)+b^(2)-c^(2))x(x^(2)+y^(2)-z^(2))+y(-x^(2)-y^(2)+z^(2))-z(x^(2)+y^(2)-z^(2))

RD SHARMA-ALGEBRAIC EXPRESSIONS AND IDENTITIES-All Questions
  1. Find the product of the following pairs of polynomials: 4,\ 7x (ii...

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  2. Find the areas of rectangles with the following pairs of monomials a...

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  3. Multiply : 3a b^2c^3b y\ 5a^3b^2c (ii) 4x^2y z\ b y-3/2x^2y z^2

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  4. Multiply : -8/5x^2yz^3b y-3/4x y^2z (ii) 3/(14)x^2y b y7/2x^4y

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  5. Find the volume of the rectangular boxes with following length, brea...

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  6. Multiply: -6a^2b c ,2a^2b\ a n d-1/4 (ii) 4/9a^5b^2,\ 10 a^3b\ a n...

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  7. Multiply: 3,15 x\ a n d-23 x^2y (ii) x , x^2y z\ a n d-3/7x y z^2

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  8. Find each of the following products: (-2x^2)xx(7a^2x^7)xx(6a^5x^5) ...

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  9. Multiply each of the monomial : 3x y z ,5x ,0

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  10. Multiply each of the monomial : 6/5a b ,5/6b c ,(12)/9a b c

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  11. Multiply each of the monomial : 3/4x^2y z^2,\ 0. 5 x y^2z^2,\ 1. 16 x^...

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  12. Multiply each of the monomial : 20 x^(10)y^(20)z^(30),\ (10 x y z)^2

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  13. Multiply each of the monomial : (-3x^2y),\ (4x y^2z),\ (-x y^2z^2)a n ...

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  14. Express the following product as a monomial : (x^3)xx(7x^5)xx(1/5x^2)x...

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  15. Multiply -4/3x^3 by 6/7x^2y and verify your result for x=2\ a n d\ y=1...

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  16. Find the product of -5x^2y ,-2/3x y^2z ,8/(15)x y z^2a n d-1/4zdot Ver...

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  17. Find the value of (5a^6)\ xx\ (-10 a b^2)\ xx\ (-2. 1 a^2b^3)\ for\ a...

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  18. Find each of the following products: 5x^2xx4x^3 (2) -3a^2xx\ 4b^4

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  19. Find each of the following products: (-5x y)xx(-3x^2y z) (2) 1/2x y...

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  20. Find each of the following products: (-7/5x y^2z)xx((13)/3x^2y z^2) ...

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