1.

Factorise `p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2)`.

Answer» Given expression : `p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2)`
Here, `x^(2)` is common in first two terms and (-a) is common in last two terms.
`therefore p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2)=x^(2)(p^(2)+c^(2))-a(c^(2)+p^(2))`
`=x^(2)(p^(2)+c^(2))-a(p^(2)+c^(2))=(p^(2)+c^(2))(x^(2)-a)`


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