Question

Wzory skróconego mnożenia:[
proszę pomózcie mi to ważne
(x+3y)² - 9y² =
4x²+1-(2x+1)²=
2(3+x)² - 12x =
(x-2)² - (x+1)² =
(x+2)² + (x-2)²=
(x+3)² - (x-3)² =
(5x+4y)² - (4x-5y)2=
(3x-2)² +2(x+3)²=
(x²+1)² - 2(x² -1)²=
2(x-y) (x+y) -3(x-2y)²=
5(x+3y) (3y-x) -2-(x+2y)²=
(x-3)² -(x+4) (4-x) - 6(3-x)=
(5-2x)² + (x+√5) (x-√5) - 5(x+2)²=

Answer 1

(x+3y)² - 9y² = x²+6xy+y²-9y²=x²+6xy-8y²
4x²+1-(2x+1)²=4x²+1-(4x²+4x+1)=4x²+1-4x²-4x-1=-4x
2(3+x)² - 12x =2(9+6x+x²)-12x=18+12x+2x²-12x=18+2x²
(x-2)² - (x+1)² =x²-4x+4-(x²+2x+1)=x²-4x+4-x²-2x-1)=-6x+3
(x+2)² + (x-2)²=x²+4x+4+x²-4x+4=2x²+8
(x+3)² - (x-3)² =x²+6x+9-(x²-6x+9)=x²+6x+9-x²+6x-9=12x
(5x+4y)² - (4x-5y)2=25x²+20xy+16y²-(16x²-40xy+25y²)=25x²+20xy+16y²-16x²+40xy-25y²=9x²-9y²+60xy
(3x-2)² +2(x+3)²=9x²-12x+4+2(x+6x+9)=9x²-12x+4+2x+12x+18=9x²+2x+22
(x²+1)² - 2(x² -1)²=x⁴+2x²+1-2(x⁴-2x²+1)=x⁴+2x²+1-2x⁴+4x²+2=-x⁴+6x²+3
2(x-y) (x+y) -3(x-2y)²=2(x²-y²)-3(x²-4y+4y²)=2x²-2y²-3x²+12y-12y²=-14y²-x²+12y
5(x+3y) (3y-x) -2-(x+2y)²=5(9y²-x²)-2-(x²-4y+4y²)=45y²-5x²-2-x²+4y-4y²=41y²-6x²+4y-2
(x-3)² -(x+4) (4-x) - 6(3-x)=(x²-6x+9)-16+x²-18+6x=2x²-25
(5-2x)² + (x+√5) (x-√5) - 5(x+2)²= 25-20x+4x²+x²-5-5(x²-4x+4)=
-20x+4x²+x²-5-5x²+20x-20=-25

Answer 2

(x+3y)² - 9y² = x² + 6xy + 9y² - 9y² = x² + 6xy

4x²+1-(2x+1)²= 4x²+1- (4x² + 4x + 1) = 4x²+1- 4x² - 4x - 1 = - 4x

2(3+x)² - 12x = 2 (9 + 6x + x²) - 12x = 18 + 12x + 2x² - 12x = 18 + 2x²

(x-2)² - (x+1)² = x² - 4x + 4 - x² - 2x - 1 = -6x + 3

(x+2)² + (x-2)²= x² + 4x + 4 + (x² - 4x + 4) = x² + 4x + 4 + x² - 4x + 4 = 2x² + 8

(x+3)² - (x-3)² = x² + 6x + 9 - (x² - 6x + 9) = x² + 6x + 9 - x² + 6x - 9 = 12x

(5x+4y)² - (4x-5y)2= 25x² + 40xy + 16y² - (16x² - 40xy + 25y²)2= 25x² + 40xy + 16y² - 32x² + 80xy - 50y² = -7x² + 120xy - 34y²

(3x-2)² +2(x+3)²= 9x² - 12x + 4 + 2(x² + 6x + 9) = 9x² - 12x + 4 + 2x² + 12x + 18 = 11x² + 22

(x²+1)² - 2(x² -1)²= x⁴ + 2x² + 1 -2(x⁴ - 2x² + 1) = x⁴ + 2x² + 1 - 2x⁴ + 4x² - 2 = -x⁴ + 6x² - 1

2(x-y) (x+y) -3(x-2y)²= 2 (x² - y²) - 3(x² - 4yx + 4y²) = 2x² - 2y² - 3x² + 12xy - 12y² = -x² - 14y² + 12xy

5(x+3y) (3y-x) -2-(x+2y)²= 5(9y² - x²) - 2 - (x² + 4xy + 4y²) = 45y² - 5x² - 2 - x² - 4xy - 4y² = 41y² - 6x² - 2 - 4xy

(x-3)² -(x+4) (4-x) - 6(3-x)= x² - 6x + 9 - (x² - 16) = x² - 6x + 9 - x² + 16 = -6x + 25

(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 - 4x - 4 = 16 - 24x

Answer 3

1. (x+3y)²-9y²=x²+6xy+9y²-9y²=x²+6xy
2. 4x²+1-(2x+1)²=4x²+1-(4x²+4x+1)=4x²+1-4x²-4x-1=-4x
3. 2(3+x)²-12x=2(9+6x+x²)-12x=18+12x+2x²-12x²=18+2x²
4. (x-2)²-(x+1)²=x²-4x+4-(x²+2x+1)=x²-4x+4-x²-2x-1=-6x+3
5. (x+2)²+(x-2)²=x²+4x+4+x²-4x+4=2x²+8
6. (x+3)²-(x-3)²=x²+6x+9-(x²-6x+9)=x²+6x+9-x²+6x-9=12x
7. (5x+4y)²-(4x-5y)²=
=25x²+40xy+16y²-(16x²-40xy+25y²)=
=25x²+40xy+16y²-16x²+40xy-25y²=
=80xy
8. (3x-2)²+2(x+3)²=
=9x²-12x+4+2(x²+6x+9)=
=9x²-12x+4+2x²+12x+18=
=11x²+22
9. (x²+1)²-2(x²-1)²=
=x⁴+2x²+1-2(x⁴-2x²+1)=
=x⁴+2x²+1-2x⁴+4x²-2=
=-x⁴+6x²-1
10. 2(x-y)(x+y)-3(x-2y)²=
=2(x²+xy-xy-y²)-3(x²-4xy+4y²)=
=2x²+2xy-2xy-2y²-3x²+12xy-12y²=
=-x²+12xy-14y²
11. 5(x+3y)(3y-x)-2-(x+2y)²=
=5(3xy-x²+9y²-3xy)-2-(x²+4xy+4y²)=
=15xy-5x²+45y²-15xy-2-x²-4xy-4y²=
=-4xy-6x²+41y²-2
12. (x-3)²-(x+4)(4-x)-6(3-x)=
=x²-6x+9-(4x-x²+16-4x)-18+6x=
=x²-6x+9-4x+x²-16+4x-18+6x=
=2x²-25
13. (5-2x)²+(x+√5)(x-√5)-5(x+2)²=
=25-20x+4x²+x²-x√5+x√5-5-5(x²+4x+4)=
=25-20x+4x²+x²-x√5+x√5-5-5x²-20x-20=
=-40x