Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.3

Question 1

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Factorize the following .

(iv) 144x2+225y2144x^2 + 225y^2

Solution

Write as difference of squares:144x2+225y2=(12x)2(225y2)=(12x)2(15iy)2Factor:=(12x15iy)(12x+15iy)Factor out common factor 3 from each factor:=3(4x5iy)3(4x+5iy)=9(4x5iy)(4x+5iy)\begin{aligned} & \boxed{\text{Write as difference of squares:}} \\ \\ & 144x^2 + 225y^2 = (12x)^2 - (-225y^2) = (12x)^2 - (15iy)^2 \\ \\ & \boxed{\text{Factor:}} \\ \\ & = (12x - 15iy)(12x + 15iy) \\ \\ & \boxed{\text{Factor out common factor 3 from each factor:}} \\ \\ & = 3(4x - 5iy) \cdot 3(4x + 5iy) \\ \\ & = 9(4x - 5iy)(4x + 5iy) \end{aligned}