Question

Wykonaj podane działAnia a wynik doprowadzić do najprostszej postaci (przedstaw w postaci jak najprostszej sumy algebraicznej)
a) 2(a+3)(a-b)+3(b-2)(a-b)
b) 2[a-2b-5(3b-4a)]-(a-b)
c) (2a-3b+1)(8a+b)+9(a-5)
d) 5x(2-7x)-(3x+4)2x
e) 6(2-y)(5x+y)+3(x+y)(x-8)

Answer 1

A) 2(a+3)(a-b)+3(b-2)(a-b) = 2(a^2-ab+3a-3b)+3(ab+b^2-2a+2b) = 2a^2-2ab+6a-6b+3ab+3b^2-6a+6b = 2a^2+ab+3b^2

b) 2[a-2b-5(3b-4a)]-(a-b) = 2(a-2b-15b+20a)-(a-b) = 2a-2b-15b+20a-a+b = 21a-16b

c) (2a-3b+1)(8a+b)+9(a-5) = 16a^2+2ab-24ab-3b^2+8a+b+9a-45 = 16a^2-22ab-3b^2+17a+b-45

d) 5x(2-7x)-(3x+4)2x = 10x-35x^2-6x^2-8x = 2x-41x^2

e) 6(2-y)(5x+y)+3(x+y)(x-8) = 6(10x+2y-5xy-y^2)+3(x^2-8x+xy-8y) = 60x+12y-30xy-6y^2+3x^2-24x+3xy-24y = 38x-12y-27xy-6y^2+3x^2