R. D. Sharma Solutions for Chapter: Algebraic Expressions and Identities, Exercise 4: EXERCISE

Simplify:
$a\left(b-c\right)+b\left(c-a\right)+c\left(a-b\right)$

After simplifying $4ab\left(a-b\right)-6a^2\left(b-b^2\right)-3b^2\left(2a^2-a\right)+2ab\left(b-a\right)$ if we get $-k{a}^{2}b+a{b}^2$, then find the value of $k$.

After simplifying $x^2(x^2+1)-x^3(x+1)-x(x^3-x)$ we get $-x^4+k{x}^2-x^3$, then find the value of $k$.

After simplifying $2a^2+3a\left(1-2a^3\right)+a\left(a+1\right)$ we get $-k{a}^4+3a^2+4a$, then find the value of $k$.

After Simplifying $a^2\left(2a-1\right)+3a+a^3-8$ if we get, $k{a}^3-a^2+3a-8$, then find the value of $k$.

After simplifying $\frac{3}{2}{x}^2\left(x^2-1\right)+\frac{1}{4}{x}^2\left(x^2+x\right)-\frac{3}{4}x\left(x^3-1\right)$ we get $x^4+\frac{1}{4}{x}^3-\frac{3}{2}{x}^2+\frac{k}{4}x$, then find the value of $k$.

After simplifying $a^{2}b\left(a-b^2\right)+a{b}^2\left(4ab-2a^2\right)-a^{3}b\left(1-2b\right)$ we get $3a^k{b}^3$, then find the value of $k$.

Simplify
$a^{2}b\left(a^3-a+1\right)-ab\left(a^4-2a^2+2a\right)-b\left(a^3-a^2-1\right)$