Q70 of 128 Page 224

State whether the statements are true (T) or false (F).

x2 + (a+b)x + ab = (a+b) (x+ab)

We need to factorize x2 + (a + b)x + ab, by splitting the middle term:

x2 + (a + b)x + ab = x2 + ax + bx + ab [∵, ax + bx = (a + b)x & ax × bx = abx2)


⇒ x2 + (a + b)x + ab = x(x + a) + b(x + a)


⇒ x2 + (a + b)x + ab = (x + a)(x + b)


And (x + a)(x + b) ≠ (a + b)(x + ab)


⇒ x2 + (a + b)x + ab ≠ (a + b)(x + ab)


Hence, the statement is false.


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