Question

Разложить на множители 1. (p - a)²- 9p + 9a2. (m - n)²- mk + kn​

Answer 1

1). (p - a)² - 9p + 9a = (p - a)² - 9(p - a) = (p - a)(p - a - 9);

2). (m - n)² - mk + kn = (m - n)² - k(m - n) = (m - n)(m - n - k);

Answer 2

$1) \: {(p - a)}^{2} - 9p + 9a = {(p - a)}^{2} - 9(p - a) = (p - a)(p - a - 9)$

$2) \: {(m - n)}^{2} - mk + kn = {(m - n)}^{2} - k(m - n) = (m - n)(m - n - k)$

Answer 3

1. (p - a)² - 9p + 9a

To factorize this expression, let's rearrange the terms:

(p - a)² - 9p + 9a = (p² - 2pa + a²) - 9p + 9a

Now, combine like terms:

p² - 2pa + a² - 9p + 9a

Next, let's group the terms:

(p² - 2pa - 9p) + (a² + 9a)

Now, factor out common terms from each group:

p(p - 2a - 9) + a(a + 9)

The factored form of the expression (p - a)² - 9p + 9a is:

(p - a)(p - 2a - 9) + a(a + 9)

2. (m - n)² - mk + kn

Similarly, let's rearrange the terms:

(m - n)² - mk + kn = (m² - 2mn + n²) - mk + kn

Combine like terms:

m² - 2mn + n² - mk + kn

Now, group the terms:

(m² - 2mn - mk) + (n² + kn)

Factor out common terms from each group:

m(m - 2n - k) + n(n + k)

The factored form of the expression (m - n)² - mk + kn is:

(m - n)(m - 2n - k) + n(n + k)