Question

Factorize the following algebraic expressions by spliting the middle term: (x² - 5x)² - 36

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

$(x {}^{2} - 5x) {}^{2} - 36 \\ = (x {}^{2} - 5x) {}^{2} - 6 {}^{2} \\ = (x {}^{2} - 5x - 6)(x {}^{2} - 5x + 6) \\ = (x {}^{2} - 6x + x - 6)(x {}^{2} - 3x - 2x + 6) \\ = (x - 6)(x + 1)(x - 3)(x - 2)$