Question

How do you find the product ${(2b + 3)^2}$?

Answer 1

Hint: In this question they have given an expression ${(2b + 3)^2}$ and asked us to find its product. The word product itself clears that we need to do multiplication. Since the expression is given in a power, we have to split it in two and multiply it inside. The resultant will be the required product of the given expression.

Formula used: For any number been squared, we can write
${a^2} = a \times a$

Complete step-by-step solution:
Here, we are given with an expression and are asked to find its product.
The word product clearly means the multiplication. Therefore we need to multiply.
The given expression is ${(2b + 3)^2}$,
As we can see, it has a power of $2$ that is square, we have to multiply terms twice to find the product.
So we need to split this into two and then multiply this.
We know that we can write ${(2b + 3)^2}$as $(2b + 3) \times (2b + 3)$
So now,
$ \Rightarrow {(2b + 3)^2} = (2b + 3)(2b + 3)$
We have to multiply each and every number in the right hand bracket to the each and every number in the left hand bracket.
\[ \Rightarrow (2b + 3)(2b + 3) = 2b(2b + 3) + {\text{ }}3(2b + 3)\]
Multiplying the numbers inside the brackets we get,
$ \Rightarrow 4{b^2} + 6b + 6b + 9$
Adding the variables in the middle, we get
$ \Rightarrow 4{b^2} + 12b + 9$
This cannot be simply further.

Therefore $4{b^2} + 12b + 9$ is the product of ${(2b + 3)^2}$.

Note: In this question we have alternative method as follows:
This can also be solved by using a well-known formula in mathematics easily.
The formula is ${(a + b)^2} = {a^2} + 2ab + {b^2}$
Now, applying the formula in the given question, we get
$ \Rightarrow {(2b + 3)^2}$
Now we have to use the formula and we get
$ \Rightarrow {(2b + 3)^2} = {(2b)^2} + 2(2b)(3) + {3^2}$
Squaring and multiplying the brackets we get,
$ \Rightarrow {(2b + 3)^2} = 4{b^2} + 12b + 9$
This cannot be simply further.
Therefore $4{b^2} + 12b + 9$ is the product of ${(2b + 3)^2}$.