Question

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zapisz w jak najprostszej postaci:
(x +3y) kwadrat - 9y kwadrat
4x kwadrat + 1 - (2x+1) kwadrat
2(3+b) kwadrat-12 b
(x-2) kwadrat - (x+1)kwadrat
(a+2) kwadrat + (a-2)kwadrat
(b+2)kwadrat - (b-3) kwadrat
(5m +4n) kwadrat - (4m-5n) kwadrat
(3x-2) kwadrat +2(x+3) kwadrat
(y kwadrat +1) kwadrat - 2 (y kwadrat -1) kwadrat
(5- 0,2 k sześcian) kwadrat + 5(k sześcian - 5)

Answer 1

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

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

2(3+b) kwadrat-12 b
2(3+b)² -12b = 2(9+6b+b²)-12b = 18+12b+2b²-12b = 2b²+18

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

(a+2) kwadrat + (a-2)kwadrat
(a+2)²+(a-2)² = a²+4a+4+a²-4a+4 = 2a²+8

(b+2)kwadrat - (b-3) kwadrat
(b+2)²-(b-3)² = b²+4b+4-(b²-6b+9) = b²+4b+4-b²+6b-9 = 10b-5

(5m +4n) kwadrat - (4m-5n) kwadrat
(5m+4n)²-(4m-5n)² = 5m²+40mn+16n²-(16m²-40mn+25n²) = 5m²+40mn+16n²-16m²+40mn-25n² = 21m²-9n²+80mn

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

(y kwadrat +1) kwadrat - 2 (y kwadrat -1) kwadrat
(y²+1)²-2(y²-1)²= y⁴+2y²+1-2(y⁴-2y²+1) = y⁴+2y²+1-2y⁴+4y²-2 = -y⁴+6y²-1

(5- 0,2 k sześcian) kwadrat + 5(k sześcian - 5)
(5-0,2k³)²+5(k³-5) = 25-2k³+0,04k⁶+5k³-25 = 0,04k⁶+3k³