Question

Algebraic expression $3x \times \left( {4x + 2} \right)$ is equal to:

A) $12{x^2} + 6x$
B) $6\left( {2{x^2} + x} \right)$
C) $x\left( {12x + 6} \right)$
D) All of the above

Answer 1

Hint: We have an algebraic expression in one variable. We can take the product and compare them with the options. Then we can take the common factors outside the bracket and check with the other options.

Complete step by step solution: We have the expression $3x \times \left( {4x + 2} \right)$

Let $I = 3x \times \left( {4x + 2} \right)$

We can multiply $3x$with both the terms inside the bracket.

$ \Rightarrow I = 3x \times 4x + 3x \times 2$

$ \Rightarrow I = 12{x^2} + 6x$.

Now we have option A.

Now we can take the common factor of 6 from both the terms.

$ \Rightarrow I = 6 \times 2{x^2} + 6 \times x$

$ \Rightarrow I = 6\left( {2{x^2} + x} \right)$

Now, this is option B.

Now we can take x from both the terms of option A.

$ \Rightarrow I = x \times 12x + 6 \times x$

$ \Rightarrow I = x\left( {12x + 6} \right)$.

Now, this is option C.

As all the options A B and C are equal to the given expression, we can select the option All of the
above,

Therefore, the correct answer is option D.

Note: We used the concept of simple algebraic multiplication. We must keep in mind that while taking the product, we must multiply the term outside the bracket with both the term inside the bracket separately and then take the sum. Similarly, we can take a number outside the bracket only if the number is a common factor to both the terms inside the brackets. All the expression will have equal value for equal values of x.