Question

Wzory skroconego mnozenia:

1) (3^3+1)do kwadratu=

2) (5^2-3)do kwadratu=

3) (4^3) (4+^3)=

4) (4^5-2)do kwadratu=

5) (6^2+^3)do kwadratu=

6) (4^3+^5) (4^3-^5)=

^-pierwiastek

do kwadratu-2

Answer 1

1) (3√3+1)²=(3√3)² + 2*3√3*1 + 1² = 27 + 6√3+1=28+6√3

2) (5√2-3)²=(5√2)² - 2*5√2*3 + 3² = 50-30√3+9 = 59 -30√3

3) (4+√3) (4+√3)=4²-(√3)²=16-3 = 13

4) (4√5-2)²=(4√5)² - 2*4√5*2 + 2² = 80 - 16√5+4 = 84-16√5

5) (6√2+√3)²=(6√2)² + 2*6√2*√3 + (√3)² = 72 + 12√6 + 3 = 75+12√6 = 3(25+4√6)

6) (4√3+√5) (4√3-√5)= (4√3)² - (√5)² = 48 -5 = 43

 

(a+b)²=a²+2ab+b²

(a-b)²=a²-2ab+b²

(a-b)(a+b) =a²-b²

Answer 2

Rozwiązanie:

1) (3√3+1)^2=(3√3)^2 + 2*3√3*1 + 1^2 = 27 + 6√3+1=28+6√3

2) (5√2-3)^2=(5√2)^2 - 2*5√2*3 + 3^2 = 50-30√3+9 = 59 -30√3

3) (4+√3) (4+√3)=4^2-(√3)^2=16-3 = 13

4) (4√5-2)^2=(4√5)^2 - 2*4√5*2 + 2^2 = 80 - 16√5+4 = 84-16√5

5) (6√2+√3)^2=(6√2)^2 + 2*6√2*√3 + (√3)^2 = 72 + 12√6 + 3 = 75+12√6 = 3(25+4√6)

6) (4√3+√5) (4√3-√5)= (4√3)^2 - (√5)^2 = 48 -5 = 43

 

Oznaczenia:

^2-do kwadratu

 √-pierwiastek

*-razy