Question

How do you simplify ${(4x + 5)^2}$ ?

Answer 1

Hint: The given expression is an algebraic expression as it is a combination of numerical values and unknown variable quantities represented by an alphabet. In this question, x is used to express some unknown variable quantity. We don’t have to find the value of x, we have to find the square of the sum of 4x and 5, where 4x represents 4 times of x. Square of a number means that the number multiplied with itself, for example, 2 multiplied with itself gives 4, so 4 is the square of 2. Using the above-mentioned definitions, we can simplify the given algebraic expression.

Complete step-by-step solution:
We have to simplify ${(4x + 5)^2}$ that is we have to find the square of $4x + 5$ .
We know that –
$
  {(a + b)^2} = {a^2} + {b^2} + 2ab \\
   \Rightarrow {(4x + 5)^2} = {(4x)^2} + {(5)^2} + 2 \times 4x \times 5 \\
   \Rightarrow {(4x + 5)^2} = 16{x^2} + 25 + 40x \\
 $
Hence, the simplified form of ${(4x + 5)^2}$ is $16{x^2} + 25 + 40x$ .

Note: The simplified form of an expression means a more understandable and easier way of writing the expression. We can find the square of $4x + 5$ by writing ${(4x + 5)^2}$ as $(4x + 5)(4x + 5)$ then we can multiply the two brackets with each other by multiplying each term in the first bracket with the whole second bracket one by one but this process turns out to be quite long so there are several formulas for simplifying such expressions. We have used the formula that states, the square of the sum of two numbers is equal to the square of the first number plus the square of the second number plus the product of 2, first number and second number, that is, ${(a + b)^2} = {a^2} + {b^2} + 2ab$