Question

Scoateti factorul comun:
a) 15xy²- 25x²y²+ 20x²y²-55x²y⁴
b) 24a⁴b³+42a³b³-18a²b
c) 12x²y+ 8x³y³- 24xy+16x²y²

Answer 1

a)15xy²-25x²y²+20x²y²-55x²y⁴=

15xy²+(-25x²y²+20x²y²)-55x²y⁴=

15xy²-5x²y²-55x²y⁴

$b) {24a}^{4} + {42a}^{3} {b}^{3} - {18a}^{2}b = \\ \\ {6a}^{2}b( \frac{ {24a}^{4} }{ {6a}^{2}b } + \frac{ {42a}^{3} {b}^{3} }{ {6a}^{2}b } + \frac{ { - 18a}^{2}b }{ {6a}^{2}b }) = \\ \\ {6a}^{2}b( {4a}^{2} {b}^{2} + {7ab}^{2} - 3)$

$c) {12x}^{2}y + {8x}^{3} {y}^{3} - 24xy + {16x}^{2} {y}^{2} = \\ \\ 4xy( \frac{ {12x}^{2}y }{4xy} + \frac{ {8x}^{3} {y}^{3} }{4xy} + \frac{ - 24xy}{4xy} + \frac{ {16x}^{2} {y}^{2} }{4xy}) = \\ \\ 4xy(3x + {2x}^{2} {y}^{2} - 6 + 4xy)$