Analyzing Mathematical Statements

The question asks us to identify the statement that is NOT true among the given options related to mathematical expressions and equations.

Statement 1: $3+4\times5$ is not a mathematical expression

A mathematical expression is a combination of numbers, variables, and mathematical operations (like addition, subtraction, multiplication, division). Following the order of operations (PEMDAS/BODMAS), multiplication is performed before addition:

• $4 \times 5 = 20$
• $3 + 20 = 23$

Since $3+4\times5$ evaluates to a specific value (23) using defined operations, it is indeed a mathematical expression. Therefore, the statement claiming it is NOT a mathematical expression is false.

Statement 2: Operations of multiplication can be done on mathematical expressions

Mathematical expressions can be combined using operations. For example, we can multiply two algebraic expressions like $(x+2)$ and $(x+3)$:

• $(x+2) \times (x+3) = x(x+3) + 2(x+3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6$

This shows that multiplication is a valid operation on mathematical expressions. This statement is true.

Statement 3: The expression $(x^2+10x+25)$ cannot be simplified further

Let's examine the expression $(x^2+10x+25)$. This is a quadratic expression. We can check if it can be factored. This expression fits the pattern of a perfect square trinomial:

• $a^2 + 2ab + b^2 = (a+b)^2$

In our case, $a^2 = x^2$ (so $a=x$) and $b^2 = 25$ (so $b=5$). Let's check the middle term: $2ab = 2(x)(5) = 10x$. This matches the middle term of the expression.

Therefore, $(x^2+10x+25)$ can be simplified (factored) as $(x+5)^2$. Since the expression *can* be simplified, the statement claiming it *cannot* be simplified further is false.

Statement 4: The value of the variable in an equation which satisfy the equation is called a solution of the equation

This is the definition of a solution to an equation. For example, in the equation $x - 3 = 7$, the value $x=10$ satisfies the equation because $10 - 3 = 7$. Thus, $x=10$ is the solution. This statement is true.

Conclusion

We are looking for the statement that is NOT true. Based on the analysis:

• Statement 1 is false.
• Statement 2 is true.
• Statement 3 is false.
• Statement 4 is true.

The question asks for the statement that is NOT true. Both statements 1 and 3 are false. However, usually in such MCQs, there's only one incorrect option intended. Let's re-evaluate. Statement 1 correctly identifies $3+4\times5$ as a mathematical expression, so saying it's NOT is false. Statement 3 says $(x^2+10x+25)$ cannot be simplified, but it can be factored into $(x+5)^2$, making the statement false. Given the provided correct answer focuses on option 3, we will highlight that.

The expression $(x^2+10x+25)$ is a perfect square trinomial and can be simplified to $(x+5)^2$. Therefore, the statement that it cannot be simplified further is incorrect.