Question

Find the square root of (8x^2 + 10x – 25)(2x^2 + 15x + 25)(4x^2 + 15x – 25)​

Answer 1

Answer:

So in Step 2 you get ((5+3x)^2 which is equivalent to (5+3x)*(5+3x).

After you distribute you get this string of numbers: 25+15x+15x+9x^2

From there you simplify to: 9x^2+30x+25.

I hope this helps! Have a good day! :D

Answer 2

Answer:

$(8x {}^{2} + 10x - 25)(2x {}^{2} + 15x + 25)(4x {}^{2} + 15x - 25)$

$= (8x {}^{2} + 20x - 10x - 25)(2x {}^{2} + 10 + 5x + 25)(4x {}^{2} + 20x - 5x - 25)$

= {4x(2x + 5) – 5(2x – 5)} {2x(x + 5) + 5(x + 5)}

{4x(x + 5) – 5(x + 5)}

= {(2x + 5)(4x – 5)} {(x + 5)(2x + 5)} {(4x – 5)(x + 5)}

= (2x + 5)(2x + 5)(4x – 5)(4x – 5)(x + 5)(x + 5)

$= \sqrt{(2x + 5) {}^{2}(4x - 5) {}^{2} (x + 5) {}^{2} }$

= (2x + 5)(4x – 5)(x + 5)

Hence, square root of (8x^2 + 10x – 25)(2x^2 + 15x + 25)(4x^2 + 15x – 25) is (2x+5)(4x–5)(x+5).

How to find?

To find the square root of a polynomial, arrange the terms with reference to the powers of some number; take the square root of the first term of the polynomial for the first term of the root, and subtract its square from the polynomial; divide the first term of the remainder by twice the root found for the next term of the root, and add the quotient to the trial divisor; multiply the complete divisor by the second term of the root, and subtract the product from the remainder. If there is still a remainder, consider the root already found as one term, and proceed as before.