what is the Factor of the perfect square trinomial 128y^2 − 192y + 72

Question

show me step by step please

Answer 1

The trinomial is 128y² - 192 y + 72

Multiply first term 128y² and last term 72 = 9216y²

The correct pair of the terms -96y and -96y multiply to 9216y² and add to -192y.

Replace the middle term -192y with - 96y - 96y.

= 128y² - 96 y - 96y + 72

Group the terms into two pairs.

= (128y² - 96 y) + (- 96y + 72)

Factor out 32y from the first group  and factor out negative 24 from the second group.

= 32y(4y - 3) - 24(4y - 3)

Factor out common term 4y - 3.

= (4y - 3)(32y - 24)

= 8(4y - 3)(4y - 3)

= 8(4y  - 3)²

Factoring of trinomial = 8(4y  - 3)²