The factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).
The given expression is 20m²/n²- 30n²/m² +1.
We need to factorise the given expression.
How to factorise the trinomial?
To factor, a trinomial in the form x²+ bx + c, find two integers, r and s, whose product is c and whose sum is b.
Rewrite the trinomial as x²+ rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).
Now, we can rewrite 20m²/n² +1 - 30n²/m² as 20m²/n² +25mn/mn- 24mn/mn- 30n²/m².
=(20m²/n² +25mn/mn)- (24mn/mn- 30n²/m²)
=5m/n(4m/n + 5m/n)-6n/m(4m/n+5n/m)
=(4m/n + 5m/n)(5m/n-6n/m)
Therefore, the factors of the given expression is (4m/n + 5m/n)(5m/n-6n/m).
To learn more about the factorisation visit:
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