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10. खण्डीकरण गर्नुस् (Factorize)
[tex]\[ y^2 - xy + x - y \][/tex]

11. \text{विएएकी बीजीय अभिव्यक्तिहरूमा साधा लगाउनुहोस्} (Find a common factor in the given algebraic expressions):
[tex]\[ m(x-y), \ n(y-x) \][/tex]

Sagot :

GinnyAnswer
Factorizing [tex]\( y^2 - xy + x - y \)[/tex]:

Step 1: Group the terms in pairs that have common factors.
[tex]\[ (y^2 - xy) + (x - y) \][/tex]

Step 2: Factor out the common factor from each pair.
[tex]\[ y(y - x) + 1(x - y) \][/tex]

Notice that [tex]\( (x - y) \)[/tex] can be seen as [tex]\(-(y - x)\)[/tex]:
[tex]\[ y(y - x) - 1(y - x) \][/tex]

Step 3: Factor out the common factor [tex]\( (y - x) \)[/tex]:
[tex]\[ (y - x)(y - 1) \][/tex]

Step 4: Simplify, keeping in mind that the negative sign distributes:
[tex]\[ - (x - y)(y - 1) \][/tex]

Therefore, the factorized form of the expression [tex]\( y^2 - xy + x - y \)[/tex] is:
[tex]\[ -(x - y)(y - 1) \][/tex]
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