F2 MATHS

Ax(x-1)(x+2) + Bx(x-1) + Cx + D = 5x* + 3X^ - 10x + 6
Ax(x^ + x -2) + B(x^ - x) + Cx + D = 5x* + 3X^ - 10x + 6
A(x* + x^ - 2x) + B(x^ - x) + Cx + D = 5x* + 3X^ - 10x + 6
Ax* + (A + B)x^ + (-2A - B + C)x + D = 5x* + 3X^ - 10x + 6

By comparing the coefficients,

A = 5
A + B = 3, therefore B = -2
-2A - B + C = -10, therefore C = -2
D = 6

54(46)
=(50 + 4)(50 - 4)
=50^ - 4^
=2500 - 16
=2484

108^ - 16(108) + 63
=(108 - 9)(108 - 7)
=99(101)
=9999

P.S. The symbols are the same as the question given.

1)Ax(x-1)(x+2)+Bx(x-1)+Cx+D = 5x³ + 3X² - 10x + 6

Ax³-Ax²+Bx²-Bx+Cx+D=5x³ + 3X² - 10x + 6

A=5 B=8 C=-2 D=6
-------------------------------------------------------------------------------------------------------
2)54(46)

=(50+4)(50-4)

=2500+200-200-16

=2516
-------------------------------------------------------------------------------------------------------
3)102² - 16(108) + 63

=102² - (62-46)(62+46) + 63

=102² - (3844+2852-2852-2116) + 63

=102² - 1728 + 63

=(100+2)² - 1728 + 63

=(10000+200-200+4) - 1728 + 63

=10004 - 1728 + 63

=8339

1)A=5 B=-2 C=-10 D=6
2) 2484
3) 9999