Question

Simplify and verify:
(m²-10m+25)(m-5);m=(-2)​

Answer 1

Answer:

$m^3-15m^2+75m-125$

Step-by-step explanation:

First, we will simplify $(m^2-10m+25)$.

$m^2-10m+25$ --> $(m-5)^2$

Now, what is $(m-5)^2(m-5)$? It's $(m-5)^3$

Using the pascal triangle method, it states that $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$(m-5)^3$ is further simplified into $m^3-15m^2+75m-125$

Let's verify it! is $m^3-15m^2+75m-125$ equal to$(m^2-10m+25)(m-5);m=(-2)$?

$(-2)^3-15(-2)^2+75(-2)-125=((-2)^2-10(-2)+25)((-2)-5)$

$-8-60-150-125=(4+20+25)(-7)$

$-343=-343$

The answer is correct!