На примере многочлена ab-2b+5a-10 объясните как выполняется разложение многочлена на множители группировки

Ab-2b+5a-10=
(подчеркиваем множители и заносим в скобки)(ab-2b)+(5a-10)=
(далее выносим за скобки общие множители b(a-2)+5(a-2)=
(видим похожие множители и группируем в скобки) (b+5)(a-2)
ab-2b+5a-10=(ab-2b)+(5a-10)=b(a-2)+5(a-2)=(b+5)(a-2)

Ab-2b+5a-10=(ab-2b)+(5a-10)=
b(a-2)+5(a-2)=(a-2)(b+5)

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ответ и Объяснение:

Нужно знать формулы сокращённого умножения:

a) a²-b² = (a-b)·(a+b);

b) (a-b)² = a²-2·a·b+b²;

c) a³+b³ = (a+b)·(a²-a·b+b²);

d) a³-b³ = (a-b)·(a²+a·b+b²);

e) (a-b)³ = a³-3·a²·b+3·a·b²-b³.

1) (a²-3)³-(a-2)·(a²+4)·(a+2) = [e)] = a⁶-3·a⁴·3+3·a²·3²-3³-(a-2)·(a+2)·(a²+4) = [a)] =

= a⁶-9·a⁴+27·a²-27-(a²-4)·(a²+4) = [a)] = a⁶-9·a⁴+27·a²-27-(a⁴-16) =

= a⁶-9·a⁴+27·a²-27-a⁴+16 = a⁶-10·a⁴+27·a²-11;

2) (b²-3)³-(b²+3)(b⁴-3·b²+9) = [e), c)] = b⁶-3·b⁴·3+3·b²·3²-3³-(b⁶+27) =

= b⁶-9·b⁴+27·b²-27-b⁶-27 = -9·b⁴+27·b²-54;

3) (m²-1)(m⁴+m²+1)-(m²-1)³ = [d), e)] = m⁶-1-(m⁶-3·m⁴·1+3·m²·1²-1³) =

= m⁶-1-(m⁶-3·m⁴+3·m²-1) = m⁶-1-m⁶+3·m⁴-3·m²+1 = 3·m⁴-3·m²;

4) (x²-2)·(x⁴+2·x²+4)-(x³-1)² = [d), b)] = x⁶-8-(x⁶-2·x³+1) =

= x⁶-8-x⁶+2·x³-1 = 2·x³-9.