Fully factorise these expressions please?

a^2 - b^2 = (a + b)(a - b)

1)
(x + y)^2 - x^2
= [(x + y) + x][(x + y) - x]
= (x + y + x)(x + y - x)
= (2x + y)(y)
= y(2x + y)

2)
x^5 - 81x
= x(x^4 - 81)
= x[(x^2)^2 - 9^2]
= x(x^2 + 9)(x^2 - 9)
= x(x^2 + 9)(x^2 - 3^2)
= x(x^2 + 9)(x + 3)(x - 3)

3)
a^2 + 3ab + 2b^2
= a^2 + 2ab + ab + 2b^2
= (a^2 + 2ab) + (ab + 2b^2)
= a(a + 2b) + b(a + 2b)
= (a + 2b)(a + b)

1) y(2x+y)
2) x(x-3)(x+3)(x^2+9)
3) (a+2b)(a+b)

(x+y)^2 -x^2

Consider the form a^2-b^2
=(a-b)(a+b)

similarly the above question can be as

=(x+y-x)(x+y+x)

=y(2x+y)


x^5-81x

= x(x^4-81)

=x(x^4 -3^4)

(Here too consider a^2-b^2 , a as x^2 and b as 3^2)

=x( (x^2)^2 -(3^2)^2)

=x (x^2 -3^2) (x^2+3^2)

=x (x-3)(x+3) (x^2+9)


a^2+3ab+2b^2

=a^2+ab+2ab+2b^2

=a(a+b) +2b(a+b)

=(a+b)(a+2b)

i couldn't figure out the first one but i got the last two

#2= x(x^2+9)(x^2-9)

#3= (a+2b)(a+b)

(x + y)^2 - x^2
= x^2 + 2xy + y^2 - x^2
= y^2 + 2xy
= y(y + 2x)

x^5 - 81x
= x(x^4 - 81)
= x[(x^2)^2 - 9^2]
= x(x^2 - 9)(x^2 + 9)

a^2 + 3ab + 2b^2
= a^2 + ab + 2ab + 2b^2
= a(a + b) + 2b(a + b)
= (a + 2b)(a + b)


Done

((x+y)+x)(x+y-x)
=(2x + y)y

x(x^4 - 81)
x(x^2 + 9)(x^2 - 9)
x(x^2 + 9)(x+3)(x-3)

(a+2b)(a+b)