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Simplify 5x (2x+3y) :
1) $10{x^2} + 15xy$
2) $10{x^4} + 15y$
3) $10{y^2} + 5xy$
4) $10{x^2} + 15x$

Last updated date: 26th Feb 2024
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IVSAT 2024
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Hint: The above problem is based on the calculation of the given expression to the reducible form.
Reducible form means that the equation could not be further divided or multiplied.
Using the properties for simplification we will solve the problem.

Complete step by step answer:
Let's define simplification in more details and then we will solve the problem.
Simplification means to simplify a complicated mathematical expression to get a single or direct answer. It is the process of replacing a mathematical expression by an equivalent one, which is simpler in form, for example,
Simplification of a fraction to an irreducible fraction, Simplification of expressions, Simplification by conjunction elimination in inference in logic yields a simpler, but generally non-equivalent formula.
We are being provided with the expression;
$ \Rightarrow 2x(5x + 3y)$
If we multiply 2x inside the bracket then we will get an expression, for which we will examine whether it could be reduced further or not.
$ \Rightarrow 10{x^2} + 15xy$ (This expression cannot be reduced furthermore, as there is no other division or multiplication could be performed)
Thus, $10{x^2} + 15xy$ is the final expression or the simplified expression.

So, the correct answer is Option 1.

Note: In the above problem there was no identity which was used to simplify the problem, but generally BODMAS rule(Bracket open division multiplication addition subtraction), algebraic identities and other formulas are used for simplification of the equations or expressions. Simplification has many applications in mathematics and in physics as well. In mathematics problems on ages, work and time etc use simplification. In the similar manner in Physics also many derivations could be simplified likewise.