a4 + 4a²b+ 4b2 9c² + 6cd² + d4 x6 +8fx3 + 16f2 25g² + 10gh³ + h6 y³ + 12ky⁴ + 36k2 49m² + 14l4m + 18 n10 + 16n5z + 64z2 81p² + 18pq5 + 910 r12 + 20r6s + 100s2 64t² + 16tw6 + w 12

Разложу выражения на множители, используя формулы сокращенного умножения:

1. $$a^4 + 4a^2b + 4b^2 = (a^2)^2 + 2 \cdot a^2 \cdot 2b + (2b)^2 = (a^2 + 2b)^2$$
2. $$9c^2 + 6cd^2 + d^4 = (3c)^2 + 2 \cdot 3c \cdot d^2 + (d^2)^2 = (3c + d^2)^2$$
3. $$x^6 + 8fx^3 + 16f^2 = (x^3)^2 + 2 \cdot x^3 \cdot 4f + (4f)^2 = (x^3 + 4f)^2$$
4. $$25g^2 + 10gh^3 + h^6 = (5g)^2 + 2 \cdot 5g \cdot h^3 + (h^3)^2 = (5g + h^3)^2$$
5. $$y^8 + 12ky^4 + 36k^2 = (y^4)^2 + 2 \cdot y^4 \cdot 6k + (6k)^2 = (y^4 + 6k)^2$$
6. $$49m^2 + 14l^4m + l^8 = (7m)^2 + 2 \cdot 7m \cdot l^4 + (l^4)^2 = (7m + l^4)^2$$
7. $$n^{10} + 16n^5z + 64z^2 = (n^5)^2 + 2 \cdot n^5 \cdot 8z + (8z)^2 = (n^5 + 8z)^2$$
8. $$81p^2 + 18pq^5 + q^{10} = (9p)^2 + 2 \cdot 9p \cdot q^5 + (q^5)^2 = (9p + q^5)^2$$
9. $$r^{12} + 20r^6s + 100s^2 = (r^6)^2 + 2 \cdot r^6 \cdot 10s + (10s)^2 = (r^6 + 10s)^2$$
10. $$64t^2 + 16tw^6 + w^{12} = (8t)^2 + 2 \cdot 8t \cdot w^6 + (w^6)^2 = (8t + w^6)^2$$

Ответ:

1. $$(a^2 + 2b)^2$$
2. $$(3c + d^2)^2$$
3. $$(x^3 + 4f)^2$$
4. $$(5g + h^3)^2$$
5. $$(y^4 + 6k)^2$$
6. $$(7m + l^4)^2$$
7. $$(n^5 + 8z)^2$$
8. $$(9p + q^5)^2$$
9. $$(r^6 + 10s)^2$$
10. $$(8t + w^6)^2$$