Question

Question #e8251

Answer 1

a.`k = 3`
b.`k = 100`
c.`k = 4`

Explanation:

cool, its very simple;)

the identity is, `a^2 - b^2 = (a-b)(a+b)`

comparing your questions to this identity,

a. `x^2−9=(x-3)(x+k)`
`=x^2−9=(x-3)(x+3)`
so here `k = 3`

b. `y^2−k=(y+10)(y−10)`
`=y^2−10^2=(y+10)(y−10)`
`=y^2−100=(y+10)(y−10)`
so here `k = 100`

c. `a^4−16=(a−2)(a+2)(a^2+k)`
now this one needs a lil simplification,
`(a^2)^2−4^2=(a^2+4)(a^2-4)`
and now, the identity can be applied again to `(a^2-4)`
that's like, `a^4−16=(a^2+4)(a−2)(a+2)`
so here `k = 4`!

hope this gives you an idea about the identity:)
-Sahar