How to factorize (y-2)^2 - 24(y-2) + 144 by taking out (y-2) first?

Question

asked Mar 18, 2024 23.9k views

1 Answer

Bjiang · Answer 1 · 2024-03-23T20:40:53+0000

Answer:

(y-14)^2

Explanation:

Given quadratic expression:

(y-2)^2 - 24(y-2) + 144

Factor out the common term (y - 2) from the first and second terms of the given expression:

$(y-2)\left[(y-2)-24\right]+144$

Simplify the second set of brackets:

$(y-2)\left[y-2-24\right]+144$

$(y-2)\left[y-26\right]+144$

(y-2)(y-26)+144

Expand the brackets:

y^2-26y-2y+52+144

y^2-28y+196

Find two numbers that sum to -28 and multiply to 196.

These two numbers are -14 and -14.

Rewrite the middle term as the sum of these two numbers:

y^2-14y-14y+196

Factor the first two terms and the last two terms separately:

y(y-14)-14(y-14)

Factor out the common term (y - 14):

(y-14)(y-14)

An expression multiplied by itself can be written as the square of the expression. Therefore:

$\large\boxed{(y-14)^2}$