Question

We want to factor the following expre
(x - 3)2 – 10(x - 3) + 25
Which pattern can we use to factor the expression

Answer 1

Step-by-step explanation:

$(x - 3)^{2} - 10(x - 3) + 25 \\ = (x - 3)^{2} - 5(x - 3) - 5(x - 3)+ 25 \\ = (x - 3) \{(x - 3) - 5 \} - 5 \{(x - 3) - 5 \} \\ = \{(x - 3) - 5 \} \{(x - 3) - 5 \} \\ = (x - 8)(x - 8) \\ \\ another \: way \\ \\ (x - 3)^{2} - 10(x - 3) + 25 \\ = (x - 3)^{2} - 2 \times 5 \times (x - 3) + {5}^{2} \\ = \{(x - 3) - 5 \}^{2} \\ = \{x - 3 - 5 \}^{2} \\ = \{x - 8 \}^{2} \\ = (x - 8)(x - 8)$