Question

Va rog mult
Am nevoie de ajutor deoarece nu am înțeles la clasa cum se face
Dau coroana
URGENT​

Answer 1

Răspuns:

Explicație pas cu pas:

2)

2x + 2y + ax + ay = 2(x + y) + a(x + y) = (x + y)(2 + a)

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bx + ax - by - ay = x(b + a) - y(b + a) = (b + a)(x - y)

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4x - 4y + ax - ay = 4(x - y) + a(x - y) = (x - y)(4 + a)

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3x + 3y - ax - ay = 3(x + y) - a(x + y) = (x + y)(3 - a)

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3)

x^3 + x^2 + x + 1 = x^2(x + 1) + (x + 1) = (x + 1)(x^2 + 1)

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x^3 + 3x^2 - x - 3 = x^2(x + 3) - (x + 3) = (x + 3)(x^2 - 1) = (x + 3)(x + 1)(x - 1)

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x^3 - 9x^2 + x - 9 = x^2(x - 9) + (x - 9) = (x - 9)(x^2 + 1)

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x^6 - x^4 - 16x^2 + 16 = x^4(x^2 - 1) - 16(x^2 - 1) = (x^2 - 1)(x^4 - 16)

= (x - 1)(x + 1)(x^2 + 4)(x^2 - 4) = (x - 1)(x + 1)(x^2 + 4)(x - 2)(x + 2)

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4)

x^3 - 16x = x(x^2 - 16) = x(x - 4)(x + 4)

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y^3 - 9y = y(y^2 - 9) = y(y + 3)(y - 3)

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9x^3 - 4x = x(9x^2 - 4) = x(3x + 2)(3x - 2)

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5x^2 - 5 = 5(x^2 - 1) = 5(x + 1)(x - 1)

Answer 2

2) a) 2x+2y+ax+ay=2(x+y)+a(x+y)=(2+a)(x+y)

b) bx+ax-by-ay=x(b+a) -y(b+a) =(x-y)(b+a)

c) 4x-4y+ax-ay=4(x-y)+a(x-y)=(4+a)(x-y)

d) 3x+3y-ax-ay=3(x+y)-a(x+y)=(3-a)(x+y)

e) ax+bx+ax²+bx²=x(a+b) +x²(a+b) =(a+b) (x+x²)=

= x(1+x) (a+b)

f) x³+x²-25x-25=x²(x+1)-25(x+1)=(x²-25)(x+1) =

= (x-5)(x+5)(x+1)

g) x³+x²-9x-9=x²(x+1)-9(x+1)=(x²-9)(x+1)=(x-3)(x+3)(x+1)

h) ax²+x²-9a-9=x²(a+1)-9(a+1)=(x²-9)(a+1)=(x-3)(x+3)(a+1)

4:

a) x³-16x=x(x²-16)=x(x-4) (x+4)

b) y³-9y=y(y²-9)=y(y-3) (y+3)

c) 9x³-4x=x(9x²-4)=x(3x-2)(3x+2)

d) 5x²-5=5(x²-1)=5(x-1)(x+1)

e) 12ax²-12a=12a(x²-1)=12a(x-1)(x+1)

f) 3x³-12x=3x(x²-4)=3x(x-2)(x+2)

g) 4x⁴-16x²=4x²(x²-4)=4x²(x-2)(x+2)

h) 5x³-45x=5x(x²-9)=5x(x-3)(x+3)

i) x⁴-36x²=x²(x²-36)=x²(x-6) (x+6)

j) 2x⁴-8x²=2x²(x²-4)=2x²(x-2)(x+2)

k) 7x³-28x=7x(x²-4)=7x(x-2)(x+2)

l) x la puterea 5-16x=x(x⁴-16)=x(x²-4)(x²+4)=

= x(x-2) (x+2)(x-2) (x+2)