F.3 Maths Factorize (5條）

Factorize each of the following expressions.

1.(a+3)2+13(a+3)(2a-1)+40(2a-1)2
=[(a+3)+8(2a-1)][(a+3)+5(2a-1)]
=(a+3+16a-8)(a+3+10a-5)
=(17a-5)(11a-2)


2.40x-28-12x2
=-12x2+40x-28
=-4(3x2-10x+7)
=-4(3x-7)(x-1)


3.(5y+6)(2y-3)+17
=10y2-15y+12y-18+17
=10y2-3y-1
=(2x-1)(5x+1)


4.(x3-27)-13(x-3)
=(x-3)(x2+3x+9)-13(x-3)
=(x-3)[(x2+3x+9)-13]
=(x-3)(x2+3x-4)
=(x-3)(x+4)(x-1)

5.(5x-3)(2x+1)-18
=10x2+5x-6x-3-18
=10x2-x-21
=(5x+7)(2x-3)

1. (a+3)^2+13(a+3)(2a-1)+40(2a-1)^2
=[(a+3)+5(2a-1)][(a+3)+8(2a-1)]
=(a+3+10a-5)(a+3+16a-8)
=(11a-2)(17a-5)

2. 40x-28-12x^2
=-4(3x^2-10x+7)
=-4(3x-7)(x-1)

3. (5y+6)(2y-3)+17
=10y^2-3y-18+17
=10y^2-3y-1
=(5y+1)(2y-1)

4. (x^2-27)-13(x-3)
=x^2-27-13x+39
=x^2-13x+12
=(x-12)(x-1)

5. (5x-3)(2x+1)-18
=10x^2-x-3-18
=10x^2-x-21
=(5x+7)(2x-3)

1. (a+3)^2+13(a+3)(2a-1)+40(2a-1)^2
=[(a+3)+5(2a-1)][(a+3)+8(2a-1)]
=(a+3+10a-5)(a+3+16a-8)
=(11a-2)(17a-5)

2. 40x-28-12x^2
=-4(3x^2-10x+7)
=-4(3x-7)(x-1)

3. (5y+6)(2y-3)+17
=10y^2-3y-18+17
=10y^2-3y-1
=(5y+1)(2y-1)

4. (x^2-27)-13(x-3)
=x^2-27-13x+39
=x^2-13x+12
=(x-12)(x-1)

5. (5x-3)(2x+1)-18
=10x^2-x-3-18
=10x^2-x-21
=(5x+7)(2x-3)