Question

3 . Factorise 125 x2- 20 y2​

Answer 1

Answer:

Step-by-step explanation:

Simplifying

125x2 + -20y2 = 0

Solving

125x2 + -20y2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20y2' to each side of the equation.

125x2 + -20y2 + 20y2 = 0 + 20y2

Combine like terms: -20y2 + 20y2 = 0

125x2 + 0 = 0 + 20y2

125x2 = 0 + 20y2

Remove the zero:

125x2 = 20y2

Divide each side by '125'.

x2 = 0.16y2

Simplifying

x2 = 0.16y2

Take the square root of each side:

x = {-0.4y, 0.4y}

Answer 2

SOLUTION

TO DETERMINE

To factorise

$\sf 125 {x}^{2} - 20 {y}^{2}$

FORMULA TO BE IMPLEMENTED

We are aware of the algebraic identity that

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

EVALUATION

Here the given expression is

$\sf 125 {x}^{2} - 20 {y}^{2}$

We factorise it as below

$\sf 125 {x}^{2} - 20 {y}^{2}$

$\sf = 5(25 {x}^{2} - 4 {y}^{2} )$

$\sf = 5 \bigg[{(5x)}^{2} - {(2y)}^{2} \bigg]$

$\sf = 5 (5x + 2y)(5x - 2y)$

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