Question

1.wykonaj mnożenie i zredukuj wyrazy podobne:
a) (x-1)(x³+x²+x+1)
b) (x+1)(x³-x²+x-1)
2.wykonaj mnożenie i zredukuj wyrazy podobne:
a)(x+7)(2x-1)
b)(2a-1)(a+4)
c)(4a-1)(2-3a)
d)(x+√5)(x-√5)
e)(2y-√3)(y+1)
f)(a+√2)(a-√3)
g)(2√2+k)(√2-k)
3.wykonaj działania:
a)(m+n)(m-2)+(m-n)(m+1)
b)(3x-2)(3x-2y+1)-4x(2x-3y+1)
c)3(m+1)(n-2)+2(n+1)(m-2)
d)x(x+1)(x+2)-x(x-1)(x-2)

liczę na szybką odpowiedź . ;)

Answer 1

Z.1
a) (x-1)(x³+x²+x+1) = x⁴+ x³ + x² + x - x³ - x² - x - 1 = x⁴- 1
b) (x+1)(x³-x²+x-1) = x⁴- x³ - x² - x + x³ + x² + x - 1 = x⁴-1
z.2
a)(x+7)(2x-1) = 2x² - x + 14x - 7
b)(2a-1)(a+4) = 2a² + 8a - a - 4
c)(4a-1)(2-3a) = 8a - 12a² - 2 + 3a = 11a - 12a² - 2
d)(x+√5)(x-√5) = x² - x√5 +x√5 - 5 = x² - 5
e)(2y-√3)(y+1) = 2y² + 2y - y√3 - √3
f)(a+√2)(a-√3) = a² - a√3 + a√2 - √6
g)(2√2+k)(√2-k) = 4 - 2k√2 + k√2 - 2k = 4 - k√2 - 2k
z.3
a)(m+n)(m-2)+(m-n)(m+1) = m² - 2m + mn - 2n + m² - mn + m - n = 2m² - m - 3m
b)(3x-2)(3x-2y+1)-4x(2x-3y+1) = 9x² - 6xy + 3x - 6x + 4y - 2 - 8x² + 12xy - 4x = x² + 6xy - 7x + 4y - 2
c)3(m+1)(n-2)+2(n+1)(m-2) = 3mn - 6m + 3n - 6 + 2mn - 4n + 2m - 4 = mn - 4m - n - 10
d)x(x+1)(x+2)-x(x-1)(x-2) =x³ + x² + 2x² + 2x -x³ +x² +2x² - 2x = 6x²

Answer 2

1.a)(x-1)(x³+x²+x+1)=x⁴+x³+x²+x-x³-x²-x-1=x⁴-1
b)(x+1)(x³-x²+x-1)=x⁴-x³+x²-x+x³-x²+x-1=x⁴-1
2.a)(x+7)(2x-1)=2x²-x+14x-7=2x²+13x-7
b)(2a-1)(a+4)=2a²+8a-a-4=2a²+7a-4
c)(4a-1)(2-3a)=8a-12a²-2+3a=11a-12a²-2
d)(x+√5)(x-√5)=x²-√5x+√5x-5=x²-5
e)(2y-√3)(y+1)=2y²+2y-√3y-√3
f)(a+√2)(a-√3)=a²-√3a+√2a-√6=a²-√a-√6
g)(2√2+k)(√2-k)=4-2√2k+√2k-k²
3.a)(m+n)(m-2)+(m-n)(m+1)=m²-2m+nm-2n+m²+m-nm-n=2m²-2m-2n
b)(3x-2)(3x-2y+1)-4x(2x-3y+1)=9x²-6xy+3x-6x+4y-2-8x²+12xy-4x=x²+6xy-3x+4y
c)3(m+1)(n-2)+2(n+1)(m-2)=3(mn-2m+n-2)+2(nm-2n+m-2)=3mn-6m+3n-6+2mn-4n+2m-4=5mn-4m-n-6
d)x(x+1)(x+2)-x(x-1)(x-2)=x(x²+2x+x+2)-x(x²-2x-x+2)=x³+2x²+x²+2x-x³+2x²+x²-2x=4x²+2x²