Question

How do you find the product of \[{\left( {a + 4b} \right)^2}\]?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division and to find the product of the equation, as it is in the form \[{\left( {a + b} \right)^2}\]with its expansion as \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\] hence, apply the formula to get the product.

Complete step-by-step solution:
Let us write the given equation
\[{\left( {a + 4b} \right)^2}\]
As the given equation is of the form \[{\left( {a + b} \right)^2}\], hence let us equate and find the product by expanding the terms of the given equation.
We know that
\[\Rightarrow {\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]
Substituting the value of a and b as
\[\Rightarrow {a^2} + 2\left( a \right)\left( {4b} \right) + {\left( {4b} \right)^2}\]
Hence, evaluating the terms we get
\[\Rightarrow {a^2} + 8ab + 16{b^2}\]
Therefore, the product of \[{\left( {a + 4b} \right)^2}\] is
\[\Rightarrow {a^2} + 8ab + 16{b^2}\].

Hence the correct answer is \[ {a^2} + 8ab + 16{b^2}\].

Note: Multiplication is a method of finding the product of two or more values. In arithmetic, multiplication of two numbers represents the repeated addition of one number with respect to another. Integers are the whole numbers but it does not include fractions. The integer can be either positive integer or negative integer. Here we have used the algebraic identities to solve and also we have similar algebraic identity with different sign i.e, \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]