Question

27*29 = __________ (calculate without direct calculation).

(a) 783

(b) 753

(c) 763

(d) 793

I had been asked this question by my school teacher while I was bunking the class.

My question comes from Factorisation of Polynomials and Algebraic Identities in division Polynomials of Mathematics – Class 9

Answer 1

Correct answer is (a) 783

The best explanation: We know that (a+b)*(a+c) = a^2 + (b+c)a + bc

27*29 can also be written as (25+2)*(25+4)

Now using above identity, 27*29 = (25+2)*(25+4)

= 25^2 + (2+4)25 + (4)(2)

= 625 + 6(25) + 8

= 625 + 150 + 8

= 783.