Question

factor the polynomial below.
$m^{2}-16m + 64$
show your work here
hint: to add an exponent ($x^{y}$), type \exponent\ or press \^\.
$2(m - 8)^{2}$
$2(m + 8)^{2}$
$(m - 64)^{2}$
$(m - 8)^{2}$
factor the expression.
$100-9m^{2}$
show your work here
enter your answer

Explanation:

Step1: Recall perfect - square trinomial formula

The perfect - square trinomial formula is \(a^{2}-2ab + b^{2}=(a - b)^{2}\). For the polynomial \(m^{2}-16m + 64\), we have \(a = m\) and \(2ab=16m\). Since \(a = m\), then \(2b = 16\), so \(b = 8\), and \(b^{2}=64\). So \(m^{2}-16m + 64=(m - 8)^{2}\).

Step2: Recall difference - of - squares formula

The difference - of - squares formula is \(a^{2}-b^{2}=(a + b)(a - b)\). For the expression \(100-9m^{2}\), we can rewrite it as \(10^{2}-(3m)^{2}\), where \(a = 10\) and \(b = 3m\).
So \(100-9m^{2}=(10 + 3m)(10-3m)\).

Answer:

1. For \(m^{2}-16m + 64\), the answer is \((m - 8)^{2}\)
2. For \(100-9m^{2}\), the answer is \((10 + 3m)(10-3m)\)