Question

factorise 25x^2 - 64y^2

Answer 1

25x^2 - 64y^2

=(5x)^2 - (8y)^2

=(5x+8y)(5x-8y)

Hope it helps! :)

Answer 2

Answer:

(5x + 8y) and (5x - 8y) are factors of given expression.

Step-by-step explanation:

Given expression,

$25 {x}^{2} - 64 {y}^{2}$

We know,

$25 = 5 \times 5 = {5}^{2}$

and $64 = 8 \times 8 = {8}^{2}$

Now,

$25 {x}^{2} - 64 {y}^{2} = {5}^{2} {x}^{2} - {8}^{2} {y}^{2}$

$= {(5x)}^{2} - {(8y)}^{2}$

$= (5x + 8y)(5x - 8y)$

Therefore (5x + 8y) and (5x - 8y) are factors of given expression.

Here we used formulas of Basic Algebra and power of indices.

Some formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

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

Some formulas of power of indices,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$