Question

1)$(x-\frac{y}{2})^{2}$ 2)$(a +t)^{3}$ 3)$(a^{3}c-b^{2})(a^{3}c - b^{2} )$ 4)$(y+2xy)^{2}$ 5)$(\frac{k}{3}+p^{2} )(\frac{k}{3}-p^{2} )$

Answer 1

1°) $(x - \frac{y}{2} )^{2} = x^{2} - \frac{2xy}{2} + \frac{y^{2} }{4} = x^{2} - xy + \frac{y ^{2} }{4}$

2°) $(a + t) ^{3} = a^{3} + 3a^{2}t +3at^{2} + t ^{3}$

3°) $(a^{3}c-b^{2})(a^{3}c - b^{2} ) = (a^{3}c-b^{2})^{1} \times (a^{3}c - b^{2} )^{2} = (a^{3}c-b^{2})^{1 + 1} = (a^{3}c-b^{2}) {}^{2}$

4°) $(y+2xy)^{2} = {y}^{2} + 2y \times 2xy + (2xy)^{2} = y^{2} + 4xy^{2} + 4x^{2} y^{2}$

5°) $(\frac{k}{3}+p^{2} )(\frac{k}{3}-p^{2} ) = (\frac{k}{3})^{2} - ({p}^{2})^{2} = \frac{k^{2} }{9}-p^{4}$

Espero que tenha ajudado! :)