1. Uprość wyrażenie i zredukuj wyrazy podobne:
a) (x + 5) (x – 7) =
b) (a – b) (a + 4) (11 – b) =
c) (x2 – 3) (4 – x) =
d) (5x – 7)(2x + 3) - (4x – 2)8 =
2. Oblicz:
a) pole i obwód prostokąta o bokach 3x-5 i 2x + 4


Odpowiedź :

1.

[tex]a)\\(x+5)(x-7) = x^{2}-7x+5x-35 = x^{2}-2x-35\\\\b)\\(a-b)(a+4)(11-b) =\\\\= (a-b)(11a-ab+44-4b) =11a^{2}-a^{2}b+44a-4ab -11ab+ab^{2}-44b+4b^{2} =\\\\=11a^{2}-a^{2}b+ab^{2} +4b^{2}+40a -15ab-44b[/tex]

[tex]c)\\(x^{2}-3)(4-x) = 4x^{2}-x^{3}-12+3x = -x^{3}+4x^{2}+3x-12\\\\d)\\(5x-7)(2x+3)-(4x-2)\cdot8 = 10x^{2}+15x-14x-21-32x+16 =10x^{2}-31x-5[/tex]

2.

[tex]a = 3x - 5\\b = 2x+4\\\\P = ab\\\\P = (3x-5)(2x+4) = 6x^{2}+12x-10x-20 = 6x^{2}+2x-20[/tex]

[tex]Obw = 2a + 2b=2(a+b)\\\\Obw = 2(3x-5+2x+4) = 2(5x-1) = 10x-2[/tex]