Oefeningen niveau 2

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Ontbind zo ver mogelijk in factoren.

$ 4a^3 - 25a =\answer [onlineshowanswerbutton]{a(2a - 5)(2a + 5) } $

$ x^4 - 1 =\answer [onlineshowanswerbutton]{(x - 1)(x + 1)(x^2 + 1) } $

$ 18y^5 - 2y^3 =\answer [onlineshowanswerbutton]{2y^3 (3y - 1)(3y + 1) } $

$ 32a^3 b - 50ab^3 =\answer [onlineshowanswerbutton]{2ab(4a - 5b)(4a + 5b) } $

$ 144x^3 - x =\answer [onlineshowanswerbutton]{x(12x - 1)(12x + 1) } $

$ 16a^4 - 9b^4 =\answer [onlineshowanswerbutton]{(2a - \sqrt {3} b)(2a + \sqrt {3} b)(4a^2 + 3b^2)} $

$ -a^2 - 2ab - b^2 =\answer [onlineshowanswerbutton]{-(a + b)^2 } $

$ 4x^5 - 28x^4 + 49x^3 =\answer [onlineshowanswerbutton]{x^3 (2x - 7)^2 } $

$ 8x^4 y - 24x^3 y^3 + 18x^2 y^5 =\answer [onlineshowanswerbutton]{2x^2 y(2x - 3y^2)^2 } $

$ (2x^2 + 3)(x + 1) - (x^2 + 4)(x + 1) =\answer [onlineshowanswerbutton]{(x + 1)^2 (x - 1) } $

Ontbind in factoren.

$ (x + y)^2 - 16 =\answer [onlineshowanswerbutton]{(x + y - 4)(x + y + 4) } $

$ (x + 2y)^2 - 25y^2 =\answer [onlineshowanswerbutton]{(x - 3y)(x + 7y) } $

$ (x + 1)^2 - 6(x + 1) + 9 =\answer [onlineshowanswerbutton]{(x - 2)^2 } $

$ 4(2x + 3)^2 - 20(2x + 3) + 25 =\answer [onlineshowanswerbutton]{(4x + 1)^2 } $

$ 9(5x - y)^2 - 16(3x + 2y)^2 =\answer [onlineshowanswerbutton]{(3x - 11y)(27x + 5y) } $

Ontbind in factoren. Geef voorrang aan de snelste ontbindingstechniek.

$ 9x^2 - 81x^2 y^2 =\answer [onlineshowanswerbutton]{9x^2 (1 - 3y)(1 + 3y) } $

$ x^3 + x^2 - 4x - 4 =\answer [onlineshowanswerbutton]{(x + 1)(x - 2)(x + 2) } $

$ -x^6 - 4x^4 - 4x^2 =\answer [onlineshowanswerbutton]{-x^2 (x^2 + 2)^2 } $

$ a^2 - (a + b + c)^2 =\answer [onlineshowanswerbutton]{-(b + c)(2a + b + c) } $

$ x^8 - 81 =\answer [onlineshowanswerbutton]{(x - \sqrt {3})(x + \sqrt {3})(x^2 + 3)(x^4 + 9) } $

$ a^2 (a^2 - 3) - 4(a^2 - 3) =\answer [onlineshowanswerbutton]{(a - \sqrt {3})(a + \sqrt {3})(a - 2)(a + 2) } $

$ (2x - 2)(3x + 4) - (x - 1)(2x - 1) =\answer [onlineshowanswerbutton]{(x - 1)(4x + 9) } $

$ -\sqrt {14} x^3 y + \sqrt {21} x^2 y + \sqrt {35} x^2 y^2 =\answer [onlineshowanswerbutton]{\sqrt {7} x^2 y(-\sqrt {2} x + \sqrt {3} + \sqrt {5} y) } $

$ -18s^2 t^3 + 84s^2 t^2 - 98s^2 t =\answer [onlineshowanswerbutton]{-2s^2 t(3t - 7)^2 } $

$ ac^2 + bd^2 - ad^2 - bc^2 =\answer [onlineshowanswerbutton]{(a - b)(c - d)(c + d) } $

$ (3x + 4)^2 - 8(3x + 4) + 16 =\answer [onlineshowanswerbutton]{9x^2 } $

$ x^3 - x^2 - x + 1 =\answer [onlineshowanswerbutton]{(x - 1)^2 (x + 1) } $

$ 2x^3 - 13x^2 - 6x + 39 =\answer [onlineshowanswerbutton]{(2x - 13)(x - \sqrt {3})(x + \sqrt {3}) } $

$ (5x + 1)^2 + 4(5x + 1) =\answer [onlineshowanswerbutton]{5(5x + 1)(x + 1) } $

$ ax^2 + bx^2 - 4a - 4b =\answer [onlineshowanswerbutton]{(a + b)(x - 2)(x + 2) } $

$ (4x^2 + 1)^2 - (12x - 8)(4x^2 + 1) =\answer [onlineshowanswerbutton]{(4x^2 + 1) (2x - 3)^2 } $

$ \sqrt {8} - ab + \sqrt {2} b - 2a =\answer [onlineshowanswerbutton]{(b + 2)(\sqrt {2} - a) } $

$ a^3 + b^3 + a^2 b^2 + ab =\answer [onlineshowanswerbutton]{(a + b^2)(a^2 + b) } $

$ (a + 2b)^2 - (2a - b)^2 =\answer [onlineshowanswerbutton]{(3a + b)(-a + 3b) } $

$ (a - b)^3 + (a + b)^3 =\answer [onlineshowanswerbutton]{2a(a^2 + 3b^2) } $