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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.
Answer:
[tex](4x-1)^2[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]16x^2-8x+1[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:
Therefore, two numbers are: -4 and -4
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 16x^2-4x-4x+1[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 4x(4x-1)-1(4x-1)[/tex]
Factor out the common term (4x - 1):
[tex]\implies (4x-1)(4x-1)[/tex]
Apply the exponent rule: aa = a²
[tex]\implies (4x-1)^2[/tex]
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