Question

Using the suitable identity find the following product: \[(2x - 5)(2x - 5)\]

Answer 1

Hint: Here in the given question, we need to find the product between the brackets, the property which will be used here is associative property, which says, while opening the bracket each term of first bracket will be multiplied with whole second bracket and thus simplified further.

Formulae Used: The associative property says:
\[
 (a + b)(a - b) \\
a(a - b) + b(a - b) \\
 \]

Complete step by step answer:
Here in the given question, we need to solve for the product of two brackets, in order to find the solution we are going to use the above discussed identity here and then solve it further.
Here, \[a = 2x - 5\] and \[b = 2x - 5\].
Substituting the values in the identity, we get
\[
  (2x - 5)(2x - 5) = {(2x - 5)^2} \\
   \Rightarrow {(2x - 5)^2} = {\left( {2x} \right)^2} - 2 \times 2x \times 5 + {\left( 5 \right)^2} \\
   \Rightarrow {(2x - 5)^2} = 4{x^2} - 20x + 25 \]
Here we get the simplified value for the given expression.
Additional Information: The above question is solved according to the property used, and here we obtain a quadratic equation as answer, if asked then we can solve further here by using applicable rules and properties.

Note: Here in the above given question we need to simplify the brackets, here to solve the product of two brackets, it is important to understand the associative property, in order to solve correctly and to get the right answer with the right sign attached with the numbers.