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TEA [102]
2 years ago
13

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

Mathematics
2 answers:
Gennadij [26K]2 years ago
7 0

Answer:

(4x-1)^2

Step-by-step explanation:

Given <u>quadratic expression</u>:

16x^2-8x+1

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

  • ac = 16 \times 1 = 16
  • b = -8

Therefore, two numbers are: -4 and -4

<u>Rewrite</u> the middle term as the sum of these two numbers:

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

<u>Factorize</u> the first two terms and the last two terms separately:

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

<u>Factor out</u> the common term (4x - 1):

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

<u>Apply</u> the exponent rule:  aa = a²

\implies (4x-1)^2

Learn more about factoring quadratics here:

brainly.com/question/27956741

brainly.com/question/27947331

dolphi86 [110]2 years ago
3 0

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.

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