If x2 - bx + c = (x + p) (x - q) , then factorise x2 - bxy + cy2

CBSE Class 9 Answered

If x² - bx + c = (x + p) (x - q) , then factorise x² - bxy + cy²

Asked by Topperlearning User | 12 Sep, 2017, 12:18: PM

Expert Answer

$begin mathsize 12px style straight x squared space minus space bx plus straight c space equals space left parenthesis straight x plus straight p right parenthesis space left parenthesis straight x minus straight q right parenthesis space equals straight x squared space plus space open parentheses straight p minus straight q close parentheses space straight x space minus pq Equating space coefficients space of space straight x squared space and space straight x comma space we space get minus straight b space equals space straight p minus straight q space and space straight c equals negative pq Substituting space the space values space of space straight b space and space straight c space in space straight x squared minus bxy plus cy squared space equals space straight x squared plus open parentheses straight p minus straight q close parentheses space xy space minus pqy squared equals straight x squared space plus space pxy minus qxy minus space pqy squared equals straight x space open parentheses straight x space plus space py close parentheses space minus space qy space open parentheses straight x plus py close parentheses equals open parentheses straight x space minus space qy close parentheses space open parentheses straight x plus py close parentheses end style$

Answered by | 12 Sep, 2017, 02:18: PM