Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.3

Question 1

auto_storiesAcademic Material

Factorize the following .

(iii) 3x2+3y23x^2 + 3y^2

Solution

Factor out common factor 3:3x2+3y2=3(x2+y2)Write as difference of squares:x2+y2=x2(iy)2=(xiy)(x+iy)Therefore:3x2+3y2=3(xiy)(x+iy)\begin{aligned} & \boxed{\text{Factor out common factor 3:}} \\ \\ & 3x^2 + 3y^2 = 3(x^2 + y^2) \\ \\ & \boxed{\text{Write as difference of squares:}} \\ \\ & x^2 + y^2 = x^2 - (iy)^2 = (x - iy)(x + iy) \\ \\ & \boxed{\text{Therefore:}} \\ \\ & 3x^2 + 3y^2 = 3(x - iy)(x + iy) \end{aligned}