Question

25(x+y)^2-36(x-2y)^2+factorise

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\: \: \: \: \: \: \mathtt{25(x + y) {}^{2} - 36(x - 2y) {}^{2} } \\ \\ \mathtt{ = \{(5) {}^{2} (x + y) {}^{2} \} - \{(6) {}^{2} (x - 2y) {}^{2} \}} \\ \\ \mathtt{ = \{5(x + y) \} {}^{2} - \{6(x - 2y) \} {}^{2} } \\ \\ \mathtt{ = [ \{5(x + y) \} + \{6(x - 2y) \}] [\{5(x + y) \} - \{ 6(x - 2y)\}]} \\ \\ \mathtt{ = \{(5x + 5y) + (6x - 12y) \} \{(5x + 5y) - (6x + 12y) \}} \\ \\ \mathtt{ =( 5x + 6x + 5y - 12y) (5x - 6x + 5y + 12y)} \\ \\ \mathtt{ = (11x - 7y)( - x + 17y)} \\ \\ \mathtt{ = (11x - 7y)(17y - x)}$