Question

Zapisz w jak najprostszej postaci ;> :

a) (x + 1) (x - 2) + (x + 2) (x - 1)
b) (5k + n) (k-2n) - k (4k + n)
c) (4y + 3) (y - 2) - 2y (4 - 2y)
d) 2a (3a² - 1) - (a² + 2)
e) 5x² (x² +1) - (x² - 2) (x² + 3)
f) (ap - 3r) (p +2r) - (3p -r) (p + 6r)
g) 4 (2a -b) (2a + 4b) - (3a - 2b) (3b - 2a)
h) 2d² - (3c - 2d) (c - d) - c (c - 2d ) + 2d²

Answer 1

A) (x + 1) (x - 2) + (x + 2) (x - 1) = x²-x-2+x²-2+x = 2x²-4
b) (5k + n) (k-2n) - k (4k + n) = 5k²-10kn+kn-2n²-4k²-kn = k²-10kn-2n²
c) (4y + 3) (y - 2) - 2y (4 - 2y)= 4y²-8y+3y-6-8y+4y²=-6-13y
d) 2a (3a² - 1) - (a² + 2)=6a³-2a-a²-2
e) 5x² (x² +1) - (x² - 2) (x² + 3) = =5x⁴+5x²-(x⁴+3x²-2x²-6)=5x⁴+5x²-x⁴-3x²+2x²+6=4x⁴+4x²+6
f) (ap - 3r) (p +2r) - (3p -r) (p + 6r)=ap²+2rap-3rp-6r²-(3p²+18rp-rp-6r²) = ap²+2rap-3rp-6r²-3p²-18rp+rp+6r²=ap²+2rap-20rp-3p²
g) 4 (2a -b) (2a + 4b) - (3a - 2b) (3b - 2a) = 4*(4a²+8ab-2ab-4b²) -(9ab-6a²-6b²+4ab)=16a²+32ab-8ab-16b²-9ab+6a²+6b²-4ab =22a²-ab-10b²
h) 2d² - (3c - 2d) (c - d) - c (c - 2d ) + 2d² = 2d²-(3c²-3cd-2cd+2d²)-c²+2cd+2d²=2d²-3c²+3cd+2cd-2d²-c²+2cd+2d²=2d²-4c²+7cd