Question

Faktorkanlah bentuk-bentuk berikut ini !
a.p²-25
b.49-y²
c.a²-46²
d.4x²-49y²
e.25p²-16q²
f.81p²-100q²
g.a⁴-16
h.16x⁴-81y⁴
i.3a⁴-48
j.80-5p⁴
k.(m-n)²-1
l.p²-(q+r)²
m.(a+b)²-(a-b)²
n.4(x-y)²-(x+y)²

Answer 1

A. p²-25 = (p+5)(p-5)
b. 49-y² = (7+y)(7-y)
c.a²-46² = (a+46)(a-46)
d.4x²-49y² = (2x+7y)(2x-7y)
e.25p²-16q² = (5p+4q)(5p-4q)
f.81p²-100q² = (9p+10q)(9p-10q)
g.a⁴-16 = (a+4)(a-4)
h.16x⁴-81y⁴ (4x²+9y²)(4x²-9y²) = (4x²+9y²)(2x+3y)(2x-3y)
i.3a⁴-48 = 3(a⁴-16) = 3(a²+4)(a²-4) = 3(a²+4)(a+4)(a-4)
j.80-5p⁴ = 5(16-p⁴) = 5(4+p²)(4-p²) = 5(4+p²)(2+p)(2-p)
k.(m-n)²-1 = (m-n+1)(m-n-1)
l.p²-(q+r)² = (p+q+r)(p-q-r)
m.(a+b)²-(a-b)² = (a+b+a-b)(a+b-a+b) = 2(a+b)(2b) = (a+b)(4b)
n.4(x-y)²-(x+y)² = [2(x-y) + (x+y)].[2(x-y) - (x+y)] = [2x-2y+x+y].[2x-2y-x-y] = [3x-y].[x-3y]