Write the common factor: the square of 5m (a-b) - the square of 10m (a-b)

Write the common factor: the square of 5m (a-b) - the square of 10m (a-b)

5m^2（a-b)-10m(a-b)^2
=5m(a-b){m-2(a-b)}
=5m(a-b)(m-2a+2b)

The square of (AB + b) and the square of (a + 1) = the common factor
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The square of (b (a + 1)) (the square of (a + 1))
=The square of B * (a + 1) the square of - (a + 1)
=Square of (B-1) * (a + 1)
=Square of (B-1) (B + 1) (a + 1)

Proof: the equation x square + (a + 2b) x + AB = 0 has real roots

（a+2b)^2-4ab=a^2+4b^2>=0
It is known from the theorem that quadratic equation of one variable has real roots
Quadratic equation AX ^ 2 + BX + C = 0 (a ≠ 0)
If △ = B ^ 2-4ac ≥ 0), then the equation has two real roots