6 Вправа 6Алгебра 8 клас Тарасенкова 2025 · Розділ 1 · стор. 6

6. Розкладіть многочлен на множники.

1) ${\displaystyle 3a^2-3b^2=}$${\displaystyle 3(a^2-b^2)=}$${\displaystyle 3\left(a-b\right)\left(a+b\right)}$;

2) ${\displaystyle 9x^3-x=}$${\displaystyle x(9x^2-1)=}$${\displaystyle x\left(3x-1\right)\left(3x+1\right)}$;

3) ${\displaystyle y^6-y^2=}$${\displaystyle y^2(y^4-1)=}$${\displaystyle y^2\left(y^2-1\right)\left(y^2+1\right)}$;

4) ${\displaystyle 8z^3-2z=}$${\displaystyle 2z(4z^2-1)=}$${\displaystyle 2z\left(2z-1\right)\left(2z+1\right)}$;

5) ${\displaystyle n^2+10n+25=}$${\displaystyle n^2+2\cdot n\cdot 5+5^2=}$${\displaystyle {\left(n+5\right)}^2}$;

6) ${\displaystyle 4m^2-28m+49=}$${\displaystyle {\left(2m\right)}^2-2\cdot 2m\cdot 7+7^2=}$${\displaystyle {\left(2m-7\right)}^2}$;

7) ${\displaystyle 0,25+0,81x^2-0,9x=}$${\displaystyle 0,81x^2-0,9x+0,25=}$${\displaystyle {(0,9x)}^2-2\cdot 0,9x\cdot 0,5+{0,5}^2=}$${\displaystyle {\left(0,9x-0,5\right)}^2}$;

8) ${\displaystyle -60xy+45y+20x^{2}y=}$${\displaystyle 5y(-12x+9+4x^2)=}$${\displaystyle 5y(4x^2-12x+9)=}$${\displaystyle 5y{\left(2x-3\right)}^2}$;

9) ${\displaystyle a^2-b^2+a+b=}$${\displaystyle (a^2-b^2)+(a+b)=}$${\displaystyle (a-b)\left(a+b\right)+\left(a+b\right)=}$${\displaystyle \left(a+b\right)\left(a-b+1\right)}$;

10) ${\displaystyle z^2-4z+4-16z^2=}$${\displaystyle {\left(z-2\right)}^2-{\left(4z\right)}^2=}$${\displaystyle (z-2-4z)(z-2+4z)=}$${\displaystyle \left(-3z-2\right)\left(5z-2\right)}$;

11) ${\displaystyle c^3+125=}$${\displaystyle c^3+5^3=}$${\displaystyle \left(c+5\right)\left(c^2-5c+25\right)}$;

12) ${\displaystyle 27a^3-8=}$${\displaystyle {\left(3a\right)}^3-2^3=}$${\displaystyle \left(3a-2\right)\left(9a^2+6a+4\right)}$.