45 Вправа 45Алгебра 8 клас Бевз 2025 · § 1 · стор. 13

45. Розклади на множники вираз.

а) ${\displaystyle x^2-16=}$${\displaystyle x^2-4^2=}$${\displaystyle \left(x-4\right)\left(x+4\right)}$;

б) ${\displaystyle x^2-9y^4=}$${\displaystyle x^2-{\left(3y^2\right)}^2=}$${\displaystyle \left(x-3y^2\right)\left(x+3y^2\right)}$;

в) ${\displaystyle x^2-6x+9=}$${\displaystyle x^2-2\cdot x\cdot 3+3^2=}$${\displaystyle {\left(x-3\right)}^2}$;

г) ${\displaystyle a^3-4a=}$${\displaystyle a(a^2-4)=}$${\displaystyle a\left(a-2\right)\left(a+2\right)}$;

ґ) ${\displaystyle 3a^2-6ab+3b^2}$=

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

д) ${\displaystyle 2x+2y-ax-ay=}$${\displaystyle (2x+2y)-(ax+ay)}$=

=${\displaystyle 2(x+y)-a(x+y)=}$${\displaystyle \left(x+y\right)\left(2-a\right)}$.