Operations on Like and Unlike terms

Q.

What is an algebraic expression?

Q.

Express the statement as an algebraic expression.

A number increased by $9$ and multiplied by $15$

Q. One-fifth of the product of $p$ and $q$ added to the difference of $m$ and $n$. Form an algebraic expression for the given statement.

1. $\frac{1}{5}pq$
   
2. $m-n$
3. $\frac{1}{5}pq+(m+n)$
   
4. $\frac{1}{5}pq+(m-n)$
   

Q. Sum of numbers $a$ and $b$ subtracted from their product. Form an algebraic expression.

1. $a+b-ab$
2. $ab-(a+b)$

Q.

Write the expression for the following cases:

Add $a$ and $b$ and subtract the sum from $x$

Q. How many terms are there in the algebraic expression $5x+4y-20?$

1. $2$
2. $3$
3. $4$
4. $5$

Q.

Write algebraic expressions that involve.

(c) multiplication and addition.

Q. Which among the following algebraic expressions cannot be further simplified?

1. $3\times (a+b)+6ab+8a$
2. $5x+4y+7\times (x+y)$
3. $81p+49q+64r$
4. $-1+3+5+6m$

Q. Simplify the expression $5x+4y-3x-7y+8x$ by collecting the like terms together.

1. $2x+3y$
2. $2x-3y$
3. $10x+3y$
4. $10x-3y$

Q. Write the algebraic expression of the following:
The sum of numbers 𝑎 and 𝑏 subtracted from their product.

Q. Simplified form of the algebraic expression $3x^2-\frac{x}{3}+\frac{x^2}{x}=$

1. $3x^2+\frac{4x}{3}$
2. $4x^2-\frac{x}{3}$
3. $3x^2+\frac{2x}{3}$
4. None of the above

Q.

Simplify: $-21x^5{y}^3÷14x^2{y}^7$.

Q. Which of the following is the simplified form of the algebraic expression $x+\frac{x}{2}+2y-\frac{y}{2}+z$

1. $\frac{3x}{2}+\frac{3y}{2}+z$
2. $\frac{x}{2}+\frac{y}{2}+z$
3. $x+\frac{x}{2}+\frac{3y}{2}+z$
4. None of the above

Q. Which of the following is the simplified form of the algebraic expression $4x^3+\frac{x^3}{2}+x{y}^2+x^{2}y$

1. $\frac{9x^3}{2}+x^2{y}^2$
2. $\frac{9x^3}{2}+x{y}^2+x^{2}y$
3. $\frac{9x^3}{2}+2x{y}^2$
4. None of the above

Q.

Simplify: $3.6a^3{b}^{2}c÷1.2a{b}^2{c}^3$.