Factoring Trinomials help!?

Question

Factor y^2 - 10y + 21 

Factor 2a^2 - 20a + 50

Answer 1

(1).

The trinomial y² - 10y + 21.

Multiply first term y² and last term 21 = 21y².

The correct pair of the terms -7y and -3y multiply to 21y² and add to -10y.

Replace the middle term -10y with -7y - 3y.

= y² -7y - 3y + 21

Group the terms into two pairs.

= (y² -7y) + (-3y + 21)

Factor out y from the first group  and factor out -3 from the second group.

= y(y -7) - 3(y - 7)

Factor out common term (y - 7).

= (y - 7)(y - 3)

Factoring of y² - 10y + 21 = (y - 7)(y - 3).

 

Answer 2

(2).

The trinomial 2a² - 20a + 50.

Multiply first term 2a² and last term 50 = 100a².

The correct pair of the terms -10a and -10a multiply to 100a² and add to -20a.

Replace the middle term -20a with -10a - 10a.

= 2a² - 10a - 10a + 50

Group the terms into two pairs.

= (2a² - 10a) + (-10a + 50)

Factor out 2a from the first group  and factor out -10 from the second group.

= 2a(a - 5) - 10(a - 5)

Factor out common term (a - 5).

= (a - 5)(2a - 10)

= (a - 5)(2)(a - 5)

= 2(a - 5)².

Factoring of 2a² - 20a + 50 = 2(a - 5)².