乘法公式做因式分解?

Question

1. 4(1-b^2-ab)-a^2=??

2. 25x^3-16x=??

3. 1/25x^3- 9 /16=??

Answer 1

(1)4(1-b2-ab)-a2=4-a2-4ab-4b2=4-(a2+4ab+4b2)=22-(a+2b)2=(2-a-2b)(2+a+2b)(2)25x3-16x=x(25x2-16)=x[(5x)2-42]=x(5x+4)(5x-4)(3)題目應該是1/25x2 - 9 /161/25x2 - 9 /16=(x/5)2 - (3/4)2=[(x/5) + 3/4][(x/5) - 3/4]

Answer 2

1.
4[1-(b^2)-ab]-(a^2)
=4-4(b^2)-4ab-(a^2)
=-{4(b^2)-4+4ab+(a^2)}
=-{4[(b^2)-1]+4ab+(a^2)}
=-{4(b-1)(b+1)+4ab+(a^2)}→用十字交乘法
=-[a+2(b+1)][a+2(b-1)]

2.
25x^3-16x
=(5^2)x[(x^2)-(4^2)]
=(5^2)x(x-4)(x+4)

2006-11-27 00:44:32 補充：
3. [(1/25)x^3]-( 9 /16)=x｛[(x/5)^2]-[(3根號x)/(4x)]^2｝=x｛(x/5)-[(3根號x)/(4x)]｝｛(x/5)+[(3根號x)/(4x)]｝