Question

use identities of factorize. 16x2-104x+169​

Answer 1

Answer: (4x-13)2

Step-by-step Explanation:

Factoring 16x2-104x+169

The first term is, 16x2 its coefficient is 16 .

The middle term is, -104x its coefficient is -104 .

The last term, "the constant", is +169

Step-1 : Multiply the coefficient of the first term by the constant 16 • 169 = 2704

Step-2 : Find two factors of 2704 whose sum equals the coefficient of the middle term, which is -104 .

-2704 + -1 = -2705

-1352 + -2 = -1354

-676 + -4 = -680

-338 + -8 = -346

-208 + -13 = -221

-169 + -16 = -185

-104 + -26 = -130

-52 + -52 = -104 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -52 and -52

16x2 - 52x - 52x - 169

Step-4 : Add up the first 2 terms, pulling out like factors :

4x • (4x-13)

Add up the last 2 terms, pulling out common factors :

13 • (4x-13)

Step-5 : Add up the four terms of step 4 :

(4x-13) • (4x-13)

Which is the desired factorization

Multiply (4x-13) by (4x-13)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (4x-13) and the exponents are :

1 , as (4x-13) is the same number as (4x-13)1

and 1 , as (4x-13) is the same number as (4x-13)1

The product is therefore, (4x-13)(1+1)

= (4x-13)2

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Answer 2

Answer:

x=13/4

Step-by-step explanation:

Let us try the Identity 2 as there a negative sign...

${(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

Using above we can write that,

$16 {x}^{2} - 104x + 169 \\ = {(4x)}^{2} - 2(4x)(13) + {(13)}^{2} = {(4x - 13)}^{2} \\ so \: by \: solving \: x = \frac{13}{4}$

I hope you are clear if not just comment and don't forget to mark my answer as the brainliest.