Question

Korzystając ze wzorów skróconego mnożenia

(a+b)²=a²+2ab+b²

(a-b)²=2²-2ab+b²

(a+b)(a-b)=a²-b²

wykonaj poniższe przykłady:

a) 2(x-y)(x+y)-3(x-2y)²

b) 5(s+3t)(3t-s)-2(s+2t)²

c) (z+0,3)²-(a+4)(4-a)-6(3-a)

d) (a-3)²+(x+√5)(x-√5)-5(x+2)²

e) (5-2x)²+(x+√5_(x-√5)-5(x+2)²

f) (2k-l²)² - 2(k+l²)(l²-k)+(k+2l²)²

daje naj :)

Answer 1

a) 2(x-y)(x+y)-3(x-2y)²= 2(x²-y²)-3(x²-4xy+4y²)=

2x²-2y² -3x²+12xy -12y²= 12xy - 14y²-x²

 

b) 5(s+3t)(3t-s)-2(s+2t)²= 5(9t²-s²)-2(s²+2st+4t²)=

45t²-5s²-2s²-4st-8t²= 37t²-7s²-4st

 

c) (z+0,3)²-(a+4)(4-a)-6(3-a)=

z² +0,6z+0,09-(16-a²)-18+6a=

z² +0,6z+0,09-16+a²-18+6a=

z²-33,91+0,6z+a²+6a

 

d) (a-3)²+(x+√5)(x-√5)-5(x+2)²=

a²-6a+9+x²-5-5(x²+4x+4)=

a²-6a+9+x²-5 -5x²-20x -20=

a²-4x²-20x-6a-16

 

e) (5-2x)²+(x+√5_(x-√5)-5(x+2)²=

25-20x+4x²+x²-5 -5(x²+4x+4) =

25-20x+4x²+x²-5- 5x²-20x -20 = -40x

 

f) (2k-l²)² - 2(k+l²)(l²-k)+(k+2l²)² =

4k²-4kl² +l^4 - 2(l^4-k²) + k²+4kl²+4l^2=

4k²-4kl² +l^4 - 2l^4+2k²+ k²+4kl²+4l^2 = 7k² +4l²

Answer 2

a) 2(x-y)(x+y)-3(x-2y)²=2(x²-y²)-3(x²-4xy+4y²)=2x²-2y²-3x²+12xy-12y²=

=-x²-14y²+12xy

b) 5(s+3t)(3t-s)-2(s+2t)²=5(9t²-s²)-2(s²+4st+t²)=45t²-5s²-2s²-8st-2t²=

=43t²-7s²-8st

c) (z+0,3)²-(a+4)(4-a)-6(3-a)=z²+0,6z+0,09-(16-a²)-18+6a=

=z²+0,6z+0,09-16+a²-18+6a=a²+z²+6a+0,6z-33,91

d) (a-3)²+(x+√5)(x-√5)-5(x+2)²=a²-6a+9+x²-5-5(x²+4x+4)=

=a²-6a+9+x²-5-5x²-20x-20=a²-4x²-6a-20x-16


e) (5-2x)²+(x+√5_(x-√5)-5(x+2)²=25-20x+4x²+x²-5-5(x²+4x+4)=

20-20x+5x²-25x²-20x-20=-20x²-40x


f) (2k-l²)² - 2(k+l²)(l²-k)+(k+2l²)²=4k²-4kl²+l⁴-2(l⁴-k²)+k²+4kl²+4l⁴=

=4k²-4kl²+l⁴-2l⁴+2k²+k²+4kl²+4l⁴=7k²+3l⁴