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RS Aggarwal Solutions Class 6 Mathematics Solutions for Algebraic Expressions Exercise 8C in Chapter 8 - Algebraic Expressions

Question 3 Algebraic Expressions Exercise 8C
  1. Add:

(i)

3a – 2b + 5c, 2a +5b – 7c, - a – b + C

(ii)

8a – 6ab + 5b, - 6a – ab – 8b, - 4a + 2ab + 3b

(iii)

2 x^{3}-3 x^{2}+7 x-8,-5 x^{3}+2 x^{2}-4 x+1,3-6 x+5 x^{2}-x^{3}

(iv)2 x^{2}-8 x y+7 y^{2}-8 x y^{2}, 2 x y^{2}+6 x y-y^{2}+3 x^{2}, 4 y^{2}-x y-x^{2}+x y^{2}

(v)

x^{3}+y^{3}-z^{3}+3 x y z,-x^{3}+y^{3}+z^{3}-6 x y z, x^{3}-y^{3}-z^{3}-8 x y z

(vi)

2+x-x^{2}+6 x^{3},-6-2 x+4 x^{2}-3 x^{3}, 2+x^{2}, 3-x^{3}+4 x-2 x^{2}

Answer:

(i) The sum of the given expressions

= (3a + 2a –a) + (-2b +5b –b) + (5c – 7c +c)

= 4a + 2b – c

(ii) The sum of the given expressions

= (8a -6a -4a) + (5b – 8b + 3b) + (-6ab –ab + 2ab)

= -2a – 5ab

(iii) The sum of the given expressions

\begin{array}{l} =\left(2 x^{3}-5 x^{3}-x^{3}\right)+\left(-3 x^{2}+2 x^{2}+5 x^{2}\right)+(7 x-4 x-6 x)+(-8+1+3) \\ =-4 x^{3}+4 x^{2}-3 x-4 \end{array}

(iv) The sum of the given expressions\begin{array}{l} =\left(2 x^{2}+3 x^{2}-x^{2}\right)+(-8 x y+6 x y-x y)+\left(7 y^{2}-y^{2}+4 y^{2}\right)+\left(-8 x y^{2}+2 x y^{2}+x y^{2}\right) \\ =4 x^{2}-3 x y+10 y^{2}-5 x y^{2} \end{array}

(v) The sum of the given expressions\begin{array}{l} =\left(x^{3}-x^{3}+x^{3}\right)+\left(y^{3}+y^{3}-y^{3}\right)+\left(-z^{3}+z^{3}-z^{3}\right)+(3 x y z-6 x y z-8 x y z) \\ =x^{3}+y^{3}-z^{3}-11 x y z \end{array}

(vi) The sum of the given expressions\begin{array}{l} =(2-6+2+3)+(x-2 x+4 x)+\left(-x^{2}+4 x^{2}+x^{2}-2 x^{2}\right)+\left(6 x^{3}-3 x^{3}-x^{3}\right) \\ =1+3 x+2 x^{2}+2 x^{3} \end{array}

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