Question

19. x2 – m2 + 6mn - 9n2​

Answer 1

Step-by-step explanation:

x²-m²+6mn-9n²

x²-m²+(2m-3n)n=0

(x-m) (x+m)+(2m-3n)n=0

x=m

2x-3n=0

x=3n/2

Answer 2

Answer:

(x+m−n)(x−m+n)

Step-by-step explanation:

Given,

{x}^{2} - {m}^{2} + 6mn - 9 {n}^{2}x

2

−m

2

+6mn−9n

2

Further simplifying,

we get,

$$\begin{lgathered}= {x}^{2} - ( {m}^{2} - 6mn + 9 {n}^{2} ) \\ \\ = {x}^{2} - ( {(m)}^{2} - 2(m)(3n) + {(3n)}^{2} )\end{lgathered}$$

Now,

we know that,

$${a}^{2} - 2ab + {b}^{2} = {(a - b)}^{2}$$

Therefore,

using this identity,

we get,

$$= {(x)}^{2} - {(m - n)}^{2}$$

Also,

we know that,

$${a}^{2} - {b}^{2} = (a + b)(a - b)$$

Therefore,

using this identity,

we get,

$$= \bold{(x + m - n)(x - m + n)}$$

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