How do you write 49x^2 – 56x + 16 in factored form?

Mar 24, 2018

$\left(7 x - 4\right) \left(7 x - 4\right)$
or
${\left(7 x - 4\right)}^{2}$

Explanation:

To factor $49 {x}^{2} - 56 x + 16$

We factor the 1st and 3rd terms

$1 x \cdot 49 x$
$7 x \cdot 7 x$

and

$1 \cdot 16$
$2 \cdot 8$
$4 \cdot 4$

Looking at the trinomial we know the second sign is positive so we will be adding the values of the factors

$7 \cdot 4 = 28$
$7 \cdot 4 = 28$

$28 + 28 = 56$

Since the first sign is negative and we are adding we need the signs for both binomials to be negative

$\left(7 x - 4\right) \left(7 x - 4\right)$