How do you factor the trinomial $16y²+8y+1$ ?

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Answer 1 · 2016-03-16T12:32:59

$color(blue)((4y +1) (4y +1 )$ is the factorised form of the expression.

$16y^2 + 8y +1$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ay^2 + by + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 16*1 =16$

and

$N_1 +N_2 = b = 8$

After trying out a few numbers we get $N_1 = 4$ and $N_2 =4$

$4*4 = 16$ , and $4+4= 8$

$16y^2 +color(green)( 8y) +1 =16y^2 +color(green)( 4y +4y )+1$

$=4y (4y +1 ) + 1 (4y +1)$

$= color(blue)((4y +1) (4y +1 )$

$color(blue)((4y +1) (4y +1 )$ is the factorised form of the expression.

How do you factor the trinomial 16y²+8y+116y²+8y+1?