Form 3 Maths Factorize

1 (a) Factorize y³ + 27

(b) Hence, factorize y³ - 7y + 6


(a) a^3+b^3= (a+b)(a^2−ab+b^2)

y³ + 27 = y³ + 3³ = (y + 3)(y^2 - 3y + 3^2)

(b) y³ - 7y + 6 = y³ + 27 - 27 - 7y + 6

= (y³ + 27) - 7y - 21

= (y + 3)(y^2 - 3y + 3^2) - 7(y + 3)

= (y + 3)(y^2 - 3y + 9 - 7)

= (y + 3)(y^2 - 3y + 27)

2013-09-29 13:55:57 補充：
4x² - 25x + 36

=(x - 4)(x - 9)

1 (a) Factorize y^3+27
Sol
y^3+27
=y^3+3^3
=(y+3)(y^2－3y+3^2)
=(y+3)(y^2－3y+9)
(b) Hence, factorize y^3－7y+6
Sol
y^3－7y+6
=(y^3+27)+(－7y－21)
=(y+3)(y^2－3y+9)－7(y+3)
=(y^3－3y+2)(y+3)
=(y－1)(y－2)(y+3)

2. (a) Factorize 4x^2－25x+36
Sol
4x^2－25x+36
=(4x－9)(x－4)
(b)Hence，factorize 4u^4－25u^2+36
Sol
4u^4－25u^2+36
=(4u^2－9)(u^2－4)
=(2u－3)(2u+3)(u－2)(u+2)