wyrażenia algebraiczne
zadanie1
wykonaj działania:
a) (x+2)(4-3x)
b) 7x-2(x+3)(5-x)
c) (-1+5x)(x-2)
d)8x(1-X2)-(x-7)(-3X2)
e)4X2-3x (7-2x) +5x
f) 1-4(X2-x+ 2) (1+X2)
zad 2
wykonaj działania:
a) -4 X2+3x(x-1) + (2x-1) (x+3)
b) 3y2 -2x (x+2y) - (x-y) (2x+y)
c) (2a-b)(a+3b)-(a-4b)(2a+b)
d) -3x (x-1)(x-2)
e) (a+2c)(a-c+2)
f)(a-c)(2a+c-3)
zad 3
Uprość wyrażenia :
a) (x-3) (x+3)+(2+x) (2-X)
b) (x+ 3/2)(x-3/2)- (x-1/2)(x+1/2)
c) (2y-3)(2y-3)-(3y-2)(3y+2)
d) (5y+1)(5y-1)-(1+5y)(1+5y)
e) (2x-y)(2x+y) - (3y-2)(3y+2)
f)(y+3x) (3x-y)-(x-5y)(5y+3)
zad4
oblicz watośc wyrażenia:
a)(x+1)(x-1)+(x+2)(x-2)-(x+3)(x-3) dla x=pierwiastek z 3
b) (1-2x)(1+2x)+ (1-3x)(1+3x)-(1-4x)(4x+1) dla x=pierwiastek z 5
c) (2x-1)(2x-1)- (2x-1)(1+2x)-(2x+1)(2x+1) dla x= pierwiastek z 2
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zadanie1
a) (x+2)(4-3x)=4x-3x²+8-6x=-3x²-2x+8
b) 7x-2(x+3)(5-x)=7x-2(5x-x²+15-3x)=7x-2(-x²+2x-15)=7x+2x²-4x+30=2x²+3x+30
c) (-1+5x)(x-2)=-x+2+5x²-10x=5x²-11x+2
d)8x(1-x²)-(x-7)(-3x²)=8x-8x³-(-3x³+21x²)=8x-8x³+3x³-21x²=-5x³-21x²+8x
e)4x²-3x (7-2x) +5x=4x²-21x+6x²=10x²-21x
f) 1-4(x²-x+ 2) (1+x²)=1-4(x²+x⁴-x-x³+2+2x²)=1-4(x⁴-x³+3x²-x+2)=1-4x⁴+4x³-12x²+4x-8=-4x⁴+4x³-12x²+4x-7
zad 2
a) -4x²+3x(x-1) + (2x-1) (x+3)=-4x²+3x²-3x+2x²+6x-x-3=x²+2x-3
b) 3y² -2x (x+2y) - (x-y) (2x+y)=3y²-2x²-4xy-2x²-xy+2xy+2y²=5y²-4x²-3xy
c) (2a-b)(a+3b)-(a-4b)(2a+b)=2a²+6ab-ab-3b²-2a²-ab+8ab+4b²=b²+4ab
d) -3x (x-1)(x-2)=-3x(x²-2x-x+2)=-3x(x²-3x+2)=-3x³+9x²-6x
e) (a+2c)(a-c+2)=a²-ac+2a+2ac-2c²+4c=a²-2c²+ac+2a+4c
f)(a-c)(2a+c-3)=2a²+ac-3a-2ac-c²+3c=2a²-c²-ac-3a+3
zad 3
a) (x-3) (x+3)+(2+x) (2-x)=x²-9+4-x²=-5
b) (x+ 3/2)(x-3/2)- (x-½)(x+½)=x²-9/4-x²-¼=-10/4=-2½
c) (2y+3)(2y-3)-(3y-2)(3y+2)=4y²-9-9y²+4=13y²-5
d) (5y+1)(5y-1)-(1+5y)(1-5y)=25y²-1-1-25y²=-2
e) (2x-y)(2x+y) - (3y-2)(3y+2)=4x²-y²-9y²+4=4x²-10y²+4
f)(y+3x) (3x-y)-(x-5y)(5y+3)=9x²-y²-5xy-3x+25y²+15y=9x²+24y²-5xy-3x+15y
zad4
a)(x+1)(x-1)+(x+2)(x-2)-(x+3)(x-3)=x²-1+x²-4-x²+9=x²+4=(√3)²+4=3+4=7
b) (1-2x)(1+2x)+ (1-3x)(1+3x)-(1-4x)(4x+1)=1-4x²+1-9x²-1+16x²=3x²+1=3*(√5)²+1=3*5+1=15+1=16
c) (2x+1)(2x-1)- (2x-1)(1+2x)-(2x-1)(2x+1)=4x²-1+4x²+1-4x²+1=-4x²+1=-4*(√2)²+1=-4*2+1=-8+1=-7