Question

1. Zapisz wyrażenie w postaci sumy.

a) (a² + v)²

b) (½x + 2y)²

c) (3x + 1)²

2. Zapisz w postaci sumy.

a) (1 + √7)²

b) (√5 + d)²

c) (2√3 + 2)²

d) (√6 + √2)²

3. Połącz wyrażenia, które są ze sobą równe.

A. (a + 5)(a + 5)

B. (√5 + 1)(1 + √5)

C. (2+ 5a)(2 + 5a)

D. (a + 1)(1 + a)

I. 4 + 20a + 25a²

II. a² + 2a + 1

III. a² + 25 + 10a

IV. 6 + 2√5

4. Zapisz w postaci sumy

a) (1 - cd)²

b) (s - √10)²

c) (k³ - 2)(k³ - 2)

d) (3 - ac)(3 - ac)

e) (⅖ - x)²

f) (4a - 5)²

g) (2√2 - 1)(2√2 - 1)

Answer 1

Zad.1


Zad.2


Zad.3

Answer 2

1.

a) (a^2 + r)^2 = (a^2)^2 + 2a^2r + r^2 = a^4 + 2a^2r + r^2
b) (1/2x + 2y)^2 = (1/2x)^2 + 2 *1/2x * 2y + (2y)^2 = 1/4 x^2 +2xy + 4y
c) (3x + 1)^2 = (3x)^2 + 6x + 1 = 9x^2 + 6x +1

2.

a) (1+pier(7)^2 = 1 + 2*pier(7) = 1+2*pier(7) + 7
b) (pier(5) + d )^2 = (pier(5)^2 + 2*pier(5)*d + d^2 = 5 + 2pier(5)*d +d^2
c) (2pier(3)+2)^2 = (2pier(3)^2 + 2*2pier(3) *2 + 4 = 4pier(3)+8pier(3) +4 = 12pier(3) + 4
d) (pier(6) + pier(2))^2 = pier(6)^2 + 2pier(6)*pier(2) + 2 = 6+2pier(12) +2 = 8+2pier(12)
3.

A III
B IV
C I
D II
bo :
A (a+5)(a+5) =(a+5)^2 = a^2 +10a+25
B (pier(5)+1)(1+pier(5)) = (pier(5)+1)^2= 5+2pier(5)+1
C (2+5a)^2 = 4+20a+25a^2
D (a+1)^2=a2+2a+1

4.
(1-cd)^2 = 1-2cd+cd
(s-pier(10))^2 = s^2 - 2^pier(10)*s+10 = s^2 - 2pier(10)s + 10
(k^s - 2)^2 = (k^s)^2 - 2*k^s*2 + 2^2 = k^2s- 4k^s+4
(3-ac)(3+ac) = (3-ac)^2 = 3^2 - 6ac+ ac^2 = 9-6ac+ac^2
(2/3-x))^2 = (2/3)^2- 2*2/3x + x^2 = 4/9-4/3x+x^2
(4a-5)^2= (4a)^2 - 40a+ 5^5 = 16a^2-40a+25
(2pier(2)-1)^2 = (2pier(2)^2 - 2*2pier(2) + 1 = 8-4pier(2) + 1

pier(x) = 
^2 =