化簡恆等式

公式：
u² -v² =(u + v)(u - v)
(u ± v)² = u² ± 2uv + v²

1.
x² - 1
= x² - 1²
= (x + 1)(x - 1)


2.
y² - 4
= y² - 2²
= (y + 2)(y - 2)


3.
25 - a²
= 5² - a²
= (5 + a)(5 - a)


4.
b² - 4
= b² - 2²
= (b + 2)(b - 2)


5.
9c² - 1
= (3c)² - 1²
= (3c + 1)(3c - 1)


6.
4p² - 25
= (2p)² -5²
= (2p + 5)(2p - 5)


7.
49q² - 4
= (7q)² - 2²
= (7q + 2)(7q - 2)


8.
25 - 16r²
= 5² -(4r)²
= (5 + 4r)(5 - 4r)


9.
81 - 16s²
= 9² - (4s)²
= (8 + 4s)(9 - 4s)


10.
64 - 49t²
= 8² -(7t)²
= (8 + 7t)(8 - 7t)


11.
a² + 10a + 25
= (a)² + 2(a)(5) + 5²
= (a + 5)²


12.
9 + 6b + b²
= (3)² + 2(3)(b) + (b)²
= (3 + b)²


13.
9x² + 12x + 4
= (3x)² + 2(3x)(2) + (2)²
= (3x + 2)²


14.
25y² + 10y + 1
= (5y)² +2(5y)(1) + (1)²
= (5y + 1)²


15.
4 + 12p + 9p²
= (2)² + 2(2)(3p) + (3p)²
= (2 + 3p)²


16.
16 + 40q + 25q²
= (4)² +2(4)(5q) + (5q)²
= (4 + 5q)²


17.
c² - 14c + 49
= (c)² - 2(c)(7)+ (7)²
= (c - 7)²


18.
d² - 4d + 4
= (d)² - 2(d)(2) + (2)²
= (d - 2)²


19.
36r² - 12r + 1
= (6r)² - 2(6r)(1) + (1)²
= (6r - 1)²


20.
4s² - 36s + 81
= (2s)² - 2(2s)(9) + (9)²
= (2s - 9)²


21.
9t² - 24t + 16
= (3t)² - 2(3t)(4)+ (4)²
= (3t- 4)²


22.
4 - 20u + 25u²
= (2)² - 2(2)(5u) + (5u)²
= (2 - 5u)²


23.
16 - 56x + 49x²
= (4)² - 2(4)(7x) + (7x)²
= (4 - 7x)²


24.
49 - 14y + y²
= (7)² - 2(7)(y) + (y)²
= (7 - y)²


25.
64 - 16a + a²
= (8)² - 2(8)(a) + (a)²
= (8 - a)²


26.
16b² - 40b + 25
= (4b)² - 2(4b)(5) + (5)²
= (4b - 5)²


27.
m² + 4m + 4
= (m)² + 2(m)(2)+ (2)²
= (m + 2)²


28.
4n² + 12n + 9
= (2n)² +2(2n)(3) + (3)²
= (2n + 3)²

28條 10分....

1.
x^2-1
=(x+1)(x-1)

2.
y^2-4
=(y-2)(y+2)

3.
25-a^2
=(5-a)(5+a)

4.
b^2-4
=(b+2)(b-2)

5.
9c^2-1
=(3c-1)(3c+1)

6.
4p^2-25
=(2p-5)(2p+5)

7.
49q^2-4
=(7q-2)(7q+2)

8.
25-16r^2
=(5-4r)(5+4r)

9.
81-16s^2
=(9-4s)(9+4s)

10.
64-49t^2
=(8-7t)(8+7t)

11.
a^2+10a+25
=(a+5)^2

12.
9+6b^2+b^2
=(b+3)^2

13.
9x^2+12x+4
=(3x+2)^2

14.
25y^2+10y+1
=(5y+1)^2

15.
4+12p+9p^2
=(3p+2)^2

16.
16+40q+25q^2
=(5q+4)^2

17.
c^2-14+49
=(c-7)^2

18.
d^2-4d+4
=(d-2)^2

19.
36r^2-12r+1
=(6r-1)^2

20.
4s^2-36s+81
=(2s-9)^2

21.
9t^2-24t+16
=(3t-4)^2

22.
4-20u+25u^2
=(5u-2)^2

23.
16-56x+49x^2
=(7x-4)^2

24.
49-14y+y^2
=(y-7)^2

25.
64-16a+a^2
=(a-8)^2

26.
16b^2-40b+25
=(4b-5)^2

27.
m^2+4m+4
=(m+2)^2

28.
4n^2+12n+9
=(2n+3)^2