Question

Expand the following ${\left( {x + 2y + 4z} \right)^2}$

Answer 1

Hint- Proceed such questions by using formula of ${\left( {a + b + c} \right)^2}$ or by using the distributive property to expand the given polynomial . Then combine all like terms if present to solve such types of questions.

Complete step by step answer:
Using identity,
${\left( {a + b + c} \right)^2} = {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ca$
Here, a = x, b = 2y and c = 4z
$ \Rightarrow {\left( {x + 2y + 4z} \right)^2} = {x^2} + {\left( {2y} \right)^2} + {\left( {4z} \right)^2} + \left( {2 \times x \times 2y} \right) + \left( {2 \times 2y \times 4z} \right) + \left( {2 \times 4z \times x} \right)$
$ \Rightarrow {\left( {x + 2y + 4z} \right)^2} = {x^2} + 4{y^2} + 16{z^2} + 4xy + 16yz + 8zx$

Note- Remember that a polynomial is expanded if no variable appears within parentheses and all like terms have been combined . Note that this question could have been done by using distributive law and then expanding with the formula of ${\left( {a + b} \right)^2}$ .