Verify : (i) x 3 + y 3 = (x + y) (x 2 – xy + y 2 ) (ii) x 3 – y 3 = (x – y) (x 2 + xy + y 2 ).

Question

cdquestions Admin · Accepted Answer

(i) It is known that,  (x + y) 3 = x 3 + y 3 + 3xy(x + y) x 3 + y 3 = (x + y) 3 - 3xy (x + y)  = (x + y) [(x + y) 2 - 3xy]  = (x + y) (x 2 + y 2 + 2xy - 3xy)  = (x + y) (x 2 + y 2 - xy)  = (x + y) (x 2 - xy + y2) (ii) It is known that,  (x - y) 3 = x 3 - y 3 - 3xy (x - y) x 3 - y 3 = (x - y) 3 + 3xy (x - y)  = (x - y) [(x - y) 2 + 3xy]  = (x - y) (x 2 + y 2 - 2xy + 3xy)  = (x - y) (x 2 + y 2 + xy)  = (x - y) (x 2 + xy + y 2 ).

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Verify : (i) x³+ y ³= (x + y) (x²– xy + y²) (ii) x ³ – y³ = (x – y) (x² + xy + y² ).

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions