В решении.
Объяснение:
1.
9х² = (3х)²;
49х² = (7х)²;
a²b² = (ab)²;
4/9 m² = (2/3 m)²;
k¹⁰ = (k⁵)²;
9(5m - 4p)² = 3²(5m - 4p)²;
m⁴n² = (m²n)²;
25e¹² = (5e⁶)²;
a²b⁴c² = (ab²c)².
2.
4 - x² = (2 - x)*(2 + x);
9x² - 1 = (3x - 1)*(3x + 1);
49x² - y² = (7x - y)*(7x + y);
a²b² - 100 = (ab - 10)*(ab + 10);
4/9 m² - 100n² = (2/3 m - 10n)*(2/3 m + 10n);
9(5m - 4p)² - 64m² = [3(5m - 4p) - 8m]*[3(5m - 4p) + 8m].
Двумя
а) 4n⁶ - m⁴n² = (2n³ - m²n)*(2n³ + m²n);
б) 4n⁶ - m⁴n² = n²(4n⁴ - m⁴) = n²(2n² - m²)*(2n² + m²);
а) 4p¹⁰ - 20p⁵z⁶ + 25z¹² = (2p⁵ - 5z⁶)² = (2p⁵ - 5z⁶)*(2p⁵ - 5z⁶);
второго не вижу.
3.
a⁴b²c² - a²b²c⁴ + a²b⁴c² - b⁴c⁴ =
= (a⁴b²c² - a²b²c⁴) + (a²b⁴c² - b⁴c⁴) =
= a²b²c²(a² - c²) + b⁴c²(a² - c²) =
= (a² - c²)*(a²b²c² + b⁴c²) =
= (a² - c²)*b²c²(a² + b²) =
=b²c²*(a - c)*(a + c)*(a² + b²).
3+3+3+4+4+4+4+5+5+5+5=45:11=9