476 Вправа 476Алгебра 8 клас Бевз 2025 · § 9 · стор. 94

476. Подай вираз у вигляді добутку трьох множників.

а) ${\displaystyle 16a^4-1}$=

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

б) ${\displaystyle 81-x^{12}}$=

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

в) ${\displaystyle {(x^2+xy+y^2)}^2-x^2{y}^2}$=

=${\displaystyle (x^2+xy+y^2-xy)(x^2+xy+y^2+xy)}$=

=${\displaystyle \left(x^2+y^2\right)\left(x+y\right)\left(x+y\right)}$;

г) ${\displaystyle a^2{b}^2-{(a^2+ab-b^2)}^2}$=

=${\displaystyle (ab-a^2-ab+b^2)(ab+a^2+ab-b^2)}$=

=${\displaystyle (b^2-a^2)(a^2+2ab-b^2)}$=

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