Question

Factor (16x^2-8x+1) Please show your work lol

Answer 1

Answer:

$(4x-1)^2$

Step-by-step explanation:

Given quadratic expression:

$16x^2-8x+1$

To factor a quadratic in the form $ax^2+bx+c$, find two numbers that multiply to ac and sum to b:

• $ac = 16 \times 1 = 16$

• $b = -8$

Therefore, two numbers are: -4 and -4

Rewrite the middle term as the sum of these two numbers:

$\implies 16x^2-4x-4x+1$

Factorize the first two terms and the last two terms separately:

$\implies 4x(4x-1)-1(4x-1)$

Factor out the common term (4x - 1):

$\implies (4x-1)(4x-1)$

Apply the exponent rule:  aa = a²

$\implies (4x-1)^2$

Learn more about factoring quadratics here:

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Answer 2

Answer:

(4x - 1)^2.

Step-by-step explanation:

16x^2 - 8x + 1

Multiplying the first and last coefficients:

16 * 1 = 16

We need 2 numbers whose product is 16 and whose sum is -8.

These are - 4 and -4.

So we now write:

16x^2 - 4x - 4x + 1

Now factor by grouping :

= 4x(4x - 1) - 1(4x - 1)

= (4x - 1)(4x - 1)

= (4x - 1)^2

This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.