急1條F.2 MATHS題

1a : Factorize a^2 - 6ab +9b^2
=(a - 3b)^2
Sol
a^2－6ab+9b^2
=(a)^2－2*a*(3b)+(3b)^2
=(a－3b)^2

1b : By using the result of a , factorize (x + 3y)^2 - 6(x + 3y)(x - y) + 9(x - y)^2
答案係4(3y - x)^2
Sol
Set x+3y=a，x－y=b
(x+3y)^2－6(x+3y)(x－y)+9(x－y)^2
=a^2－6ab+9b^2
=(a－3b)^2
=[x+3y－3(x－y)]^2
=(－2x+6y)^2
=(6y－2x)^2
=[2(3y－x)]^2
=4(3y－x)^2

1a first you need to use cross method, (a-3b)(a-3b)
You may try to remember cross method as
out side x out + in side x in side = the middle of the equation

For example:
2a^2+14ab +20b^2
= (a +5b )(2a +4b )
out side x out side = a x 4b = 4ab
in side x in side = 5b x 2a = 10ab

out side x out side + in side x in side
= 4ab +10ab
= 14ab