Free Algebraic Expressions 01 Practice Test - 7th grade 

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables $\left(likexory\right)$ and operators. According to the given question,
Three times the product of two numbers $m$ and $n$ is $3mn.$
5 is added to three times the product of two numbers $m$ and $n.$
The equation that represents this statement is $5+3mn.$

The coefficient of term $x{y}^3$ in the expression $5x^3+10x{y}^3$ is 10.

A coefficient may be either a numerical factor (like 5, -3, 25...) or an algebraic factor (like $x,y,x^{3}y$...) or a product of two or more factors (like $3xy,5x^{2}z$...) in a term of an algebraic expression.

$\therefore$ The coefficient of $x{y}^3$ in the expression $5x^3+10x{y}^3$ is 10

The terms which have the same variable raised to the same power but may only differ in numerical coefficient are called like terms.

For example:

$\left(i\right)3mand-7m\text{are like terms.}$

$\left(ii\right)zand\frac{3}{2}z\text{are like terms.}$

So, among the given set of terms,
$12xandx\text{are like terms.}$

So the general expression for this pattern is $\frac{n(n+1)}{2}$, where n is the next term and n = 1, 2, 3, 4....

[Alternatively, eliminate the options to figure out the correct answer. This is a good method while attending competitive exams where time plays a crucial role.]

 Simplify the expression:$2a-2b-10+4a+b$
$=(2a+4a)+(-2b+b)-10=6a-b-10$

Substituting  $a=5$ and $b=1$ in the above expression,

$6a-b-10$ 
$=(6\times 5)-1-10$
$=30-11$
$=19$

A trinomial is defined as a polynomial which contains three unlike terms. The expression $5a{b}^3+22abc+10bc$ has three unlike terms and hence, it is a trinomial. 

An algebraic expression is a mathematical phrase that contains numbers, variables (represented by lower case letters of the English alphabet) and operators (such as addition, subtraction, multiplication  and division). 

Here are some examples of algebraic expressions: 
$a+1,$ $a–b,$  $3x,$ $\frac{4}{3},$ etc.

Hence, $2+3x$ is an algebraic expression.

$Given,2x^2+6a–5x+10=25$

Substituting the value of x = 1 in the above equation, we get,

$2(1{)}^2+6a-5(1)+10=25$

$\Rightarrow$ 2 + 6a - 5 + 10 = 25

$\Rightarrow$ 6a  + 7 = 25 

$\Rightarrow$ 6a = 25 - 7 = 18

$\Rightarrow$ a = 3

In order to find the sum of $2mn+11xand22x+4mn$, we need to group the like terms first (we can add only the like terms).

$\Rightarrow (2mn+11x)+(22x+4mn)$
$=2mn+11x+22x+4mn$
$=(2mn+4mn)+(11x+22x)$
$=6mn+33x$

Hence, the sum is
$6mn+33x$.

An algebraic expression which contains two unlike terms is called a binomial. For example, 8 + x, xy - 4 are binomials.

An algebraic expression which contains three unlike terms is called trinomial. For example, 8 + x + y, xy - 4x + y, etc.

So, the expression, $5x^2+5x+5$, is a trinomial as this expression contains three unlike terms, which are, $5x^2$, 5x and 5.

Hence the given statement is false.