✔ 最佳答案
你好～～～
以下都是供參考而已，如有錯誤請多多指教～～
1) -2px-qx+2py+qy+3ry-3rx
= -2px - qx - 3rx + 2py + qy + 3ry
= -x(2p + q + 3r) + y(2p + q + 3r)
= (2p + q + 3r)(y - x)
2a)Expand (x+b)^2
(x + b)^2
= x^2 + 2bx + b^2
2b)Using the result of (a), expand(u^2+u+1)(u^2-u+1)
Sol: Let (u^2 + 1) be x.
(u^2 + u + 1)(u^2 - u + 1)
= (u^2 + 1 + u)(u^2 + 1 - u)
= (x + u)(x - u)
= x^2 - u^2
= (u^2 + 1)^2 - u^2
= u^4 + 2u^2 + 1 - u^2
= u^4 + u^2 + 1
2c)Hence, find the value off 111X91 without using a calculator
111 x 91
= (100 + 11) x (100 - 9)
= (100 + 1 + 10) x (100 + 1 - 10)
= (10^2 + 1 + 10)(10^2 + 1 - 10)
= (10^2 + 1)^2 - (10)^2
= 10^4 + 2(10^2) + 1^2 - 10^2
= 10^4 + 1(10^2) + 1^2
= 10000 + 100 + 1
= 10101
3)Find the value of A,B,C in the identity
3(x^2-1)+Ax≡ (B-x)(Cx-2)
Sol:
L.H.S. = 3(x^2 - 1) + Ax
= 3x^2 - 3 + Ax
= 3x^2 + Ax - 3
R.H.S. = (B - x)(Cx - 2)
= BCx - 2B - Cx^2 + 2x
= -Cx^2 + (2 + BC)x - 2B
1) -2B = -3
B = -3 / -2
B = 1.5
2) -Cx^2 = 3x^2
-C = 3
C = -3
3) (2 + BC)x = Ax
[2 + 1.5(-3)] = A
2 - 4.5 = A
A = -2.5
希望以上解答可以幫到你～～～～～
2010-10-11 21:15:44 補充：
不要緊～
2a) 那條應該做對的～
2b) (x + y + z)^2
Let (y + z) be b.
(x + y + z)^2
= (x + b)^2
= x^2 + 2bx + b^2
= x^2 + 2x(y + z) + (y + z)^2
= x^2 + 2xy + 2xz + y^2 + 2yz + z^2
= x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
