Verified answer

a) (a - 2)² - 2(a + 2)

= a² - 4a + 4 - 2a - 4

= a² - 6a

= a(a - 6)

b) (y + 5)² - y(y + 10)

= y² - 10y + 25 - y² - 10y

= - 20y + 25

= 5(- 4y + 5)

c) (x - 3)² + (x + 3)²

= x² - 6x + 9 + x² + 6x + 9

= 2x² + 18

= 2(x² + 9)

d) (a - b)² - (a + b).(a - b)

= (a - b)² - (a² - b²)

= a² - 2ab + b² - a² + b²

= - 2ab + b²

= b( - 2a + b)

a) (a-2)² - 2(a+2)

a²-4a+4-(2a+4) =

a²-4a+4-2a-4 =

a²-6a

a(a-6)

b) (y+5)² - y(y+10)

y²+10y+25-(y²+10y)=

y²+10y+25-y²-10y=

25

c) (x-3)² + (x+3)²

x²-6x+9+x²+6x+9=

2x²+18

d) (a-b)² - (a+b).(a-b)

a²-2ab+b²-(a²-ab+ab-b²)=

a²-2ab+b²-a²+ab-ab+b²=

2b²-2ab=

2b(b-a)