Oefeningen niveau 3

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Ontbind in factoren.

$ \sqrt {18} xy^2 z^3 + \sqrt {32} x^3 y^2 z =\answer [onlineshowanswerbutton]{\sqrt {2} xy^2 z(3z^2 + 4x^2) } $

$ 3x^2 + 2\sqrt {3} xy + y^2 =\answer [onlineshowanswerbutton]{(\sqrt {3} x + y)^2 } $

$ 5y^2 + 2\sqrt {10} y + 2 =\answer [onlineshowanswerbutton]{(\sqrt {5} y + \sqrt {2})^2 } $

$ 8a^2 - 4\sqrt {6} a + 3 =\answer [onlineshowanswerbutton]{(2\sqrt {2} a - \sqrt {3})^2 } $

$ \sqrt {5} - a - ab^2 + \sqrt {5} b^2 =\answer [onlineshowanswerbutton]{-(a - \sqrt {5})(b^2 + 1) } $

Ontbind in factoren.

$ a + b + 5c + 4a^2 b + 4ab^2 + 20abc =\answer [onlineshowanswerbutton]{(a + b + 5c)(1 + 4ab) } $

$ p^2 + 2pq - 3pr - 3p - 6q + 9r =\answer [onlineshowanswerbutton]{(p + 2q - 3r)(p - 3) } $

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

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

$ 4x^2 + 9y^2 - 16z^2 - 12xy =\answer [onlineshowanswerbutton]{(2x - 3y - 4z)(2x - 3y + 4z) } $

$ x^2 - 4y^2 + 20y - 25 =\answer [onlineshowanswerbutton]{(x + 2y - 5)(x - 2y + 5) } $

$ x^2 + y^2 + 2ax - 2ay - 2xy =\answer [onlineshowanswerbutton]{(x - y)(x - y + 2a) } $

$ x^6 - 2x^5 + x^4 - 4x^2 + 8x - 4 =\answer [onlineshowanswerbutton]{(x - 1)^2 (x - \sqrt {2})(x + \sqrt {2})(x^2 + 2)} $

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

$ \sqrt {3} x^2 z - y^5 + xy^2 z - \sqrt {3} xy^3 =\answer [onlineshowanswerbutton]{(xz - y^3)(\sqrt {3} x + y^2) } $

Ontbind in factoren.

$ (7x^2 + 5x - 1)^2 - (x^2 - 5x - 1)^2 =\answer [onlineshowanswerbutton]{4x(3x + 5)(2x - 1)(2x + 1) } $

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

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

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

$ 7\sqrt {7} x^6 + 21x^4 + 3\sqrt {7} x^2 + 9 =\answer [onlineshowanswerbutton]{(\sqrt {7} x^2 + 3)(7x^4 + 3) } $

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

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

$ a^6 - a^5 + \frac {1}{3} a^4 - \frac {1}{27} a^3 =\answer [onlineshowanswerbutton]{a^3 (a - \frac {1}{3})^3 } $

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

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

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

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

$ x^2 - 6x + 9 - 9y^2 =\answer [onlineshowanswerbutton]{(x - 3y - 3)(x + 3y - 3) } $

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

$ (x - 3)^2 + 8(x^2 - 9) + 16(x + 3)^2 =\answer [onlineshowanswerbutton]{(5x + 9)^2 } $