How do you factor (a^2 +1)^2 - 7(a^2 +1) +10(a2+1)2−7(a2+1)+10?

2 Answers
Farzana H.
Sep 28, 2015

a_1=1 , a_2=-1, a_3=2, a_4=-2a1=1,a2=−1,a3=2,a4=−2

Explanation:

Let (a^2+1) =x(a2+1)=x
so the eqn is x^2-7x+10=0 x2−7x+10=0
now,
x^2 -5x-2x+10=0x2−5x−2x+10=0
=>x(x-5)-2(x-5)=0⇒x(x−5)−2(x−5)=0
=>(x-2)*(x-5)=0⇒(x−2)⋅(x−5)=0
=>x-2=0 =>x=2 =>a^2+1=2 => a^2=1⇒x−2=0⇒x=2⇒a2+1=2⇒a2=1
=>a=+-1 ⇒a=±1
Again,
=>x-5=0 =>x=5 =>a^2+1=5 => a^2=4⇒x−5=0⇒x=5⇒a2+1=5⇒a2=4
=>a=+-2 ⇒a=±2

Jim H
Sep 28, 2015

(a^2+1)^2-7(a^2+1)+10 = (a+1)(a-1)(a+2)(a-2)(a2+1)2−7(a2+1)+10=(a+1)(a−1)(a+2)(a−2)

Explanation:

Let u = a^2+1u=a2+1, then the expression is:

u^2-7u+10u2−7u+10 which can be factored:

(u-2)(u-5)(u−2)(u−5)

Replacing uu, we get:

((a^2+1)-2)((a^2+1)-5)((a2+1)−2)((a2+1)−5).

We can simplify to get:

(a^2-1)(a^2-4)(a2−1)(a2−4).

Each of these is a difference of squares, so we can finish with:

(a+1)(a-1)(a+2)(a-2)(a+1)(a−1)(a+2)(a−2)

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