Question

Find the product of (0.5x - y) and (0.5x + y).

Answer 1

Hint: In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. Here brackets mean multiplication of the value within the brackets with the number outside the brackets.

Complete step-by-step answer:
To find the product of \[\left( {0.5x - y} \right)\] and \[\left( {0.5x + y} \right)\] i.e.,
\[ \Rightarrow \;\left( {0.5x - y} \right) \times \left( {0.5x + y} \right)\]
Opening the left-hand side bracket, we have
\[
   \Rightarrow 0.5x\left( {0.5x + y} \right) - y\left( {0.5x + y} \right) \\
   \Rightarrow 0.5x \times 0.5x + 0.5x \times y - \left( {y \times 0.5x + y \times y} \right) \\
   \Rightarrow 0.5 \times 0.5 \times {x^2} + 0.5xy - \left( {0.5yx + {y^2}} \right) \\
   \Rightarrow 0.25{x^2} + 0.5xy - 0.5xy - {y^2} \\
\]
By cancelling the common terms, we get
\[ \Rightarrow 0.25{x^2} - {y^2}\]
Thus, the product of \[\left( {0.5x - y} \right)\] and \[\left( {0.5x + y} \right)\]is \[0.25{x^2} - {y^2}\].

Note: This can also be done in another method i.e., by using the formula \[\left( {a - b} \right)\left( {a + b} \right) = {a^2} - {b^2}\]
\[
   \Rightarrow \left( {0.5x - y} \right)\left( {0.5x + y} \right) = {\left( {0.5x} \right)^2} - {\left( y \right)^2} \\
   \Rightarrow \left( {0.5x - y} \right)\left( {0.5x + y} \right) = 0.25{x^2} - {y^2} \\
\]
You can do either method, which will give you the same answer.