Question

5a^2 -25b^2..Factorise fully​

Answer 1

$\mathbb \: \huge \fbox {\blue{{ANSWER}}} \\ \\ \: \: \: \:\: \: \sf \: \implies \: \: \green {\fbox {5(a {}^{2} - 5b {}^{2} )} }$

→ Given equation : 5a² – 25b²

Apply formula for this : a²–b² = (a+b) (a-b)

5a² - 25b² = 5 • (a² - 5b²)

Factoring: a²- 5b²

Theory : A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \rightarrow \fbox{ \pink{5(a {}^{2} - 5b {}^{2} )}}$

Answer 2

Answer:

= 5(a^2 - 5b^2)

Step-by-step explanation: