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July 2022
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Упростите выражение : (y+5)^2-5y(2-y), 2x(5+2x^2)+(x^2-2x)^2-x^2(x-3)(x+3) ; Разложить на множители: (y-2)^2-16 , 81a^4- 1/16b^4 , 2t+t^2+2c-c^2 , 8/125x^3- -1/27y^3
Условные обозначения: ^4- обозначение степени ; 1/16 - дробь
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2407Alexa
(y+5)²-5y(2-y)=у²+10у+25-10у+5у²=6у²+25;
2x(5+2x²)+(x²-2x)²-x²(x-3)(x+3)=10х+4х³+х⁴-4х³+4х²-х²(х²-9)=10х+х⁴+4х²-х⁴+9х²=10х+13х²;
(y-2)²-16=((у-2)-4)((у-2)+4)=(у-2-4)(у-2+4)=(у-6)(у+2);
81a⁴- 1/16b⁴=(9а²-((1/4)b²))(9a²+((1/4)b²))=(3a-(1/2)b)(3a+(1/2)b)(9a²+((1/4)b²));
2t+t²+2c-c²=(2t+2c)+(t²-c²)=2(t+c)+(t-c)(t+c)=(t+c)(2+(t-c))=(t+c)(2+t-c);
8/125x³-1/27y³=(((2/5)x)-((1/3)y))(((4/25)x²+(2/5)(1/3)xy+(((1/9)y²))))=((2x/5)-(y/3))((4x²/25)+(2/15)xy+(y²/9)).
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Answers & Comments
2x(5+2x²)+(x²-2x)²-x²(x-3)(x+3)=10х+4х³+х⁴-4х³+4х²-х²(х²-9)=10х+х⁴+4х²-х⁴+9х²=10х+13х²;
(y-2)²-16=((у-2)-4)((у-2)+4)=(у-2-4)(у-2+4)=(у-6)(у+2);
81a⁴- 1/16b⁴=(9а²-((1/4)b²))(9a²+((1/4)b²))=(3a-(1/2)b)(3a+(1/2)b)(9a²+((1/4)b²));
2t+t²+2c-c²=(2t+2c)+(t²-c²)=2(t+c)+(t-c)(t+c)=(t+c)(2+(t-c))=(t+c)(2+t-c);
8/125x³-1/27y³=(((2/5)x)-((1/3)y))(((4/25)x²+(2/5)(1/3)xy+(((1/9)y²))))=((2x/5)-(y/3))((4x²/25)+(2/15)xy+(y²/9)).