Maths Questions on Algebraic Expressions for Class 8

A student need to practice maths problems. Its helps in developing problem solving skills. The problems shall not be (i) too simple, (ii) too difficult or (iii) too many. Simple problems are boring, difficult problems discourages (at times), and too many problems don't leave time for fun.

I selected following problems on algebraic expressions for my son studying in class 8.

1. The perimeter of a triangle is $6x^2-4x+9$ and two of its sides are $x^2-2x+1$ and $3x^2-5x+3$. Find the third side of the triangle.
2. Find (a) $(4x^2+5) (4x^2+5)$ (b) $(4x^2-5) (4x^2-5)$ (c) $(4x^2+5) (4x^2-5)$
3. Find quotient and remainder when we divide ($8x^4+10x^3-5x^2-4x+1$) by ($2x^2+x-1$).
4. Find the value of expression ($36x^2+25y^2-60xy$), when $x=2/3$ and $y=1/5$.
5. If $(x-\frac{1}{x}=5)$, find the value of (a) $x^2+\frac{1}{x^2}$ (b) $x^4+\frac{1}{x^4}$.
6. If $x-y=7$ and $xy=9$, find the value of $(x^2+y^2)$.