Question

Example 14: Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the
following:
(1) 501 x 502
(ii) 95 x 103​

Answer 1

Answer:

(x+a)(x+b)(x+c)

=[x

2

+(a+b)x+ab](x+c)

=x

2

(x+c)+[(a+b)x+ab](x+c)

=x

3

+x

2

c+ax

2

+bx

2

+acx+bcx+abx+a

=x

3

+(a+b+c)x

2

+(ab+bc+ca)x+abc

Answer 2

Answer:

1) 501*502

(500+1)(500+2)=(500)^2+(1+2)500+1*2

250000+1500+2

=251502

2)95*103

(100-5)(100+3)

10000+(-5+3)100+(-5)(3)

10000+(-2)100-15

10000-200-15

10000-215

=9785