Question

Factorise this (a-2)^2-16(a+2)^2

Answer 1

(a -2)² -16(a +2)²

= (a -2)² -(4)².(a +2)²

= (a -2)² - {4(a + 2)}²

we know,
x² - y² = (x - y)(x + y) from algebraic identities , use this here,

= { a - 2 + 4(a + 2) }{ a -2 -4(a +2 }

= {a -2 + 4a + 8}{ a - 2 -4a -8}

=( 5a + 6)( -3a -10)

=(5a + 6)(-3a -10)

hence (5a + 6) and (-3a -10) are the factors of (a -2)² -16(a +2)²

Answer 2

(a-2)²-16(a+2)²

→ (a-2)² - 4²(a+2)²

→ (a-2)²-{4(a+2)}²

we know that,

x² - y² = (x-y)(x+y)

→ (a-2-{4(a+2)}) (a-2+{4(a+2)})

→ (a-2-4a-8)(a-2+4a+8)

→ (-3a-10)(5a-6)

Therefore, (-3a-10) and (5a-6) are factors of the given polynomial.

Hope it helps....