Question

☆factorize ☆

(x + 2)(x² + 25) – 10x2 – 20x​

Answer 1

Let us have the step-by-step solution to your asked question. This solution is nothing but only proceeding steps correctly. First of all, it will be the best idea to learn the chapter FACTORISATION first and then come back over here to see the total solution.

SOLUTION :

(x + 2) (x² + 25) - 10x² - 20x

= (x+2) (x²+25) - 10x (x+2)

= (x+2) (x²+25-10x)

= (x+2) (x²-10x+25)

= (x+2) [x²-(5+5)x+25]

= (x+2) [x²-5x-5x+25]

= (x+2) [x(x-5)-5(x-5)]

= (x+2) (x-5)²

Answer 2

$<b><I>$(x+2)(x^2+25) - 10x^2- 20X =

(x+2)(x^2+25) -10x (x+ 2) <-- factors out -10X from the last two terms. To convince yourself, distribute
-10x(x+2) = -10X^2 - 20X . .... WATCH THE SIGNS!!!! 

Now (x+2) is a common factor in both parts of this expression. If you want, you can let z = x+2.
Then the expression can be written as z (x^2+25) - 10x(z), from which the z can be factored.

The results is (X+2) [ (x^+25 - 10x ] =
(x+2) [x^2 - 10x + 25 ] <--- re-arranging terms inside parenthesis
(x+2) ( X - 5)(X - 5 ) <--- factoring the trinomial inside the parenthesis

= (X+2)(x-5)^2

------------------------------------

CHECK: (X+2)(x-5)(x-5) = (x+2)(x^2-10x+25) =
(x+2) [(x^2+25)-10X]
(x+2)(x^2+25) - 10x(x+2)
(x+2)(x^2+25) - 10x^2 -20X

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