Question

Factorise fully 5x^2-125 Step by step please

Answer 1

Answer:

Answer= 5(x-5)(x+5)

Step-by-step explanation:

$5x^{2} -125$

step1: take 5 as a common factor.

=$5(x^{2} -25)$  (so $5x^{2}$ divide by 5 and -125 divide by 5)

step2: factorise the bracket using the difference of two squares.

= 5(x-5)(x+5)

(to factorise using the difference of two squares we first open two brackets one with plus and one with minus then, we take the square root of both terms in the bracket - in this case, square root of $x^{2}$ is x and for 25 is 5. So we put them in the two brackets that we opened before - remember that x will come first)  

Answer 2

Answer:

5(x+5)(x-5)

Step-by-step explanation:

Given : 5x² - 125

if we express 125 into its constituent prime factors,

125 = 5 x 5 x 5  = 5³

hence our expression becomes:

5x² - 125

= 5x² - (5 x 5 x 5)

= 5x² - 5³    ( factor out 5 from the equation)

= 5 (x² - 5²)   (recall the property a²- b² =  (a+b)(a-b) , apply this to our expression)

= 5(x+5)(x-5)     answer