f.3 數學問題2條

1) 28(x+y)^2 - 7(x-y)^2= 7[ 4(x+y)^2 - (x-y)^2 ]= 7{ [2(x+y)]^2 - (x-y)^2 }= 7{ [(2(x+y) + (x-y)] [2(x+y) - (x-y)] }= 7 (2x+2y+x-y) (2x+2y-x+y)= 7 (3x+y) (x+3y)2)12v - 12v^2 - 6u + 3u^2= 3u^2 - 12v^2 - (6u - 12v)= 3(u^2 - 4v^2) - 6(u - 2v)= 3(u - 2v)(u + 2v) - 6(u - 2v)= (u - 2v) (3(u + 2v) - 6)= (u - 2v) (3u + 6v - 6)= 3 (u - 2v) (u + 2v - 2)

1. 28(x+y)^2-7(x-y)^2

if a=x+y , b=x-y ,

28(x+y)^2-7(x-y)^2
=28a^2-7b^2
=7(4a^2-b^2)
=7[(2a)^2-b^2)
=7(2a+b)(2a-b)
=7(2x+2y+x-y)(2x+2y-x+y)
=7(3x+y)(x+3y)

2. 12v-12v^2-6u+3u^2

= 3u^2-12v^2 -6u+12v
=3(u^2-4v^2) -6(u-2v)
=3(u+2v)(u-2v)-6(u-2v)
=(u-2v)(3u+6v-6)
=3(u-2v)(u+2v-2)

Hope my comment can help you!!!

1.28(x+y)^2-7(x-y)^2
=28(x^2+y^2)-7(x^2-y^2)
=28x^2+28y^2-7x^2+7y^2
=28x^2-7x^2+28y^2+7y^2
=21x^2+35y^2