Question

Which of these identities can be used to factorize the expression 4x2 - 19x + 16?
a. (x - a)2 = x2 - 2a + a2
b. (x + a)2 = x2 + 2a + a2
C. (x – a)(x - b) = x2 - (a + b)x + ab
d. (x - a)(x + a) = x2 - a2​

Answer 1

Which of these identities can be used to factorize the expression 4x2 - 19x + 16?

a. (x - a)2 = x2 - 2a + a2

b. (x + a)2 = x2 + 2a + a2

C. (x – a)(x - b) = x2 - (a + b)x + ab

d. (x - a)(x + a) = x2 - a2

Answer 2

Answer:

Option C. (x – a)(x - b) = x2 - (a + b)x + ab

Step-by-step explanation:

Observe that this expressions are not of the type

(x + a)^2 or (x – a)^2 , i.e., they are not perfect squares.

For example, in x^2 + 5x + 6, the term 6 is not a perfect square. This expressions obviously also do not fit the type (x 2 – a 2 ) either. They, however, seem to be of the type C. (x – a)(x - b) = x^2- (a + b) x + a b.