Question

zapisz w jak najprostszej postaci:

a) (a+3)(a-1)+(a-7)(a+5)

b) (2b-5)(3-2b)-(3b+2)(b-6)

c) -7c^{2}(5c-4)+(3c^{2}+c)(6-2c)

d) 3m(m-4)(5m+2)-m(2m+3)(4-3m)

e) -2x(3x-5y)-(x+2y)(3x-y)

Answer 1

a) (a+3)(a-1)+(a-7)(a+5)=a²-a+3a-3+a²+5a-7a-35=2a²-38

b) (2b-5)(3-2b)-(3b+2)(b-6)=6b-4b²-15+10b-(3b²-18b+2b-12)=-4b²+16b-15-3b²+16b+12=-7b+32b-3

c) -7c^{2}(5c-4)+(3c^{2}+c)(6-2c)=-35c³+28c²+18c²-6c³+6c-2c²=29c³+44c²+6c

d) 3m(m-4)(5m+2)-m(2m+3)(4-3m)=(3m²-12m)(5m+2)-(2m²+3m)(4-3m)=

=15m³+6m²-60m²-24m-(8m²-6m³+12m-9m²)=15m³-54m²-24m+m²+6m³-12m=

=21m³-53m²-36m

e) -2x(3x-5y)-(x+2y)(3x-y)=-6x²+10xy-(3x²-xy+6xy-2y²)=-6x²-10xy-3x²-5xy+2y²=-9x²+2y²-15xy