Question

resolve into factors
${m}^{2} {n}^{2} - 6mnp + 9 {p}^{2}$

Answer 1

$\textbf{Answer :}$

Now,

m²n² - 6mnp + 9p²

= m²n² - (3 + 3)mnp + 9p²

= m²n² - 3mnp - 3mnp + 9p²

= mn (mn - 3p) - 3p (mn - 3p)

= (mn - 3p) (mn - 3p),

which is the required factorization.

Here, (mn - 3p) and (mn - 3p) are the two factors of the given polynomial.

#$\textbf{MarkAsBrainliest}$

Answer 2

$\textbf{Answer :}$ (mn - 3p)²

$\textbf{Solution :}$

“you can do it in two methods,”

✔The first one,

a² - 2ab + b² = (a - b)²

♦ m²n² - 6mnp + 9p²

= m²n² - 6mnp + 3²p²

= (mn)² - 2(mn) (3p) + (3p)²

= (mn - 3p)²

“the answer came as (mn - 3p)² because,

“according to the formula,”

a² - 2ab + b²

= (mn)² - 2(mn) (3p) + (3p)²

is equal to

(a - b)²

= (mn - 3p)²

✔The second one,

“by spliting the middle term,”

♦ m²n² - 6mnp + 9p²

[here, we can split the middle term “6mnp” by 3+3]

$\textbf{Kindly refer to the attachment}$

= m²n² - (3+3)mnp + 9p²

= m²n² - 3mnp - 3mnp + 9p²

[Now, here we need to find common factors between the first & the last two equations]

= mn(mn - 3p) - 3p(mn - 3p)

= (mn - 3p) (mn - 3p)

= (mn - 3p)²

You can use any of these two methods, whichever you feel comfortable.

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$\textbf{Hope it helps you}$

$\textbf{Have a great day ahead}$
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