Question

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Answer 1

Răspuns:

Explicație pas cu pas:

a) (6x+3)²-(5x-4)² = folosim formula a²-b²=(a-b)(a+b) =>

= (6x+3-5x+4)(6x+3+5x-4) = (x+7)(11x-1)

b) 8x³-(x-5)³ =(2x)³ - (x-5)³= folosim formula a³-b³ = (a-b)(a²+ab+b²) =>

= (2x-x+5)(4x²+2x²-10x+x²-10x+25) = (x+5)(7x²-20x+25)

c) 125x³+(x+1)³ = (5x)³+(x+1)³ =folosim formula a³+b³ = (a+b)(a²-ab+b²) =>

= (5x+x+1)(25x²-5x²-5x+x²+2x+1) = (6x+1)(21x²-3x+1)

a) x³+2x²(x-2)-8 = x³-2³ + 2x²(x-2) = (x-2)(x²+2x+4)+2x²(x-2) =

= (x-2)(x²+2x+4+2x²) = (x-2)(3x²+2x+4)

b) x⁶-4x³+4 = (x³-2)²

c) x⁵-x³+5x²+5x = x³(x²-1)+5x(x+1) = x³(x-1)(x+1)+5x(x+1) =

= (x+1)[x³(x-1)+5x] = (x+1)(x⁴-x³+5x) = x(x+1)(x³-x²+5)

d) x⁴-x²+2x+2 = x²(x²-1)+2(x+1) = x²(x+1)(x-1)+2(x+1) =

= (x+1)[x²(x-1)+2] = (x+1)(x³-x²+2)