Subject Experts Solutions for Chapter: Algebraic Expressions and Identities, Exercise 5: SUMMATIVE ASSESSMENT

If the sum of $5+x-x^2-x^3, 3x-5+2x^2-x^3$ and $x+5+2x^3-5x^2$ is of the form $a{x}^3+b{x}^2+cx+d$, then find the value of $\left(a+b+c+d\right)$.

If the expansion of $(\sqrt{3}x-2y{)}^2$ is $a{x}^2-b\sqrt{3}xy+c{y}^2$, then find the value of $a+b+c$.

The perimeter of a triangle is $6p^2-4p+9$ and two of it's adjacent side are $p^2-2p+1$ and $3p^2-5p+3$. The third side of the triangle is $2p^2+3p+k$. Find $k$.

Classify the following polynomial as monomial, binomial, and trinomial and give reason.

$5xy{z}^2-3zy$

Classify the following polynomial as monomial, binomial, and trinomial and give reason.

$\frac{a}{2}+\frac{{\displaystyle b}}{{\displaystyle 2}}-ab$

Classify the following polynomial as monomial, binomial, and trinomial and give reason.

$pqr$

Verify $(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc$

Find the value of expressions in RHS for $a=1,b=-2$ and $c=3$

In a class project, a class has to perform on Munshi prem chand's novel. The class is divided into three groups to play three acts. If number of students in three acts can be represented as $7xy+5yz-3zx, 4yz+9zx-4y$ and $-3xz+5x-2xy$. The play was executed very effectively. They were highly appreciated for their group efforts.

Write an expression representing total number of students in the class.