Question

Factorisation -

$1) \: \: \tt \: {x}^{2} - {4y}^{2}$
$2) \: \: \tt \: {9a}^{2} {x}^{2} - 9 {b}^{3}$
$3) \: \: \tt \: \frac{ {a}^{2} }{9} - \frac{ {b}^{4} }{16}$
$4) \: \: \tt \: {48x}^{3} - 27x$
$5) \: \: \tt \: 4 {a}^{2} b - 9 {b}^{3}$
$6) \: \: \tt \: {a}^{2} - 81(b - c) ^{2}$
$7) \: \: \tt \: {a}^{4} - 1$
$8) \: \: \tt \: {9a}^{2} - ( {a}^{2} - 4) ^{2}$
$9) \: \: \tt \: 2 {x}^{4} - 32$
$10) \: \: \tt \: {16x}^{2} - {y}^{2} + 4yz - {4z}^{2}$

Please solve the above.
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Answer 1

Answer:

Factorisation -

$1) \: \: \tt \: {x}^{2} - {4y}^{2}$

$2) \: \: \tt \: {9a}^{2} {x}^{2} - 9 {b}^{3}$

$3) \: \: \tt \: \frac{ {a}^{2} }{9} - \frac{ {b}^{4} }{16}$

$4) \: \: \tt \: {48x}^{3} - 27x$

$5) \: \: \tt \: 4 {a}^{2} b - 9 {b}^{3}$

$6) \: \: \tt \: {a}^{2} - 81(b - c) ^{2}$

$7) \: \: \tt \: {a}^{4} - 1$

$8) \: \: \tt \: {9a}^{2} - ( {a}^{2} - 4) ^{2}$

$9) \: \: \tt \: 2 {x}^{4} - 32$

$10) \: \: \tt \: {16x}^{2} - {y}^{2} + 4yz - {4z}^{2}$

Please solve the above. not simple please brainliest answers

Answer 2

Solutions!!

(1)

x² - 4y²

= x² - 2²y²

= (x)² - (2y)²

Use a² - b² = (a - b)(a + b).

= (x - 2y)(x + 2y)

(2)

9a²x² - 9b³

= 9(ax)² - 9b³

= 9((ax)² - b³)

(3)

(a²/9) - (b⁴/16)

= (16a² - 9b⁴)/144

= (1/144)(16a² - 9b⁴)

= (1/144)((4a)² - (3b²)²)

Use a² - b² = (a - b)(a + b).

= (1/144)(4a - 3b²)(4a + 3b²)

(4)

48x³ - 27x

= 3x(16x² - 9)

= 3x((4x)² - (3)²)

Use a² - b² = (a - b)(a + b).

= 3x(4x - 3)(4x + 3)

(5)

4a²b - 9b²

= b(4a² - 9b)

(6)

a² -81(b - c)²

Use a² - b² = (a - b)(a + b).

= (a - 9(b - c))(a + 9(b - c))

= (a - 9b + 9c)(a + 9b - 9c)

(7)

a⁴ - 1

Use a² - b² = (a - b)(a + b).

= (a² - 1)(a² + 1)

Use a² - b² = (a - b)(a + b).

= (a - 1)(a + 1)(a² + 1)

(8)

9a² - (a² - 4)²

Use a² - b² = (a - b)(a + b).

= (3a - (a² - 4))(3a + (a² - 4))

= (3a - a² + 4)(3a + a² - 4)

= (-a² + 3a + 4)(a² + 3a - 4)

= (-a² + 4a - a + 4)(a² + 4a - a - 4)

= (-a(a - 4) - (a - 4))(a(a + 4) - (a + 4))

= (-(a - 4)(a + 1))(a + 4)(a - 1)

= -(a - 4)(a + 1)(a + 4)(a - 1)

(9)

2x⁴ - 32

= 2(x⁴ - 16)

= 2((x²)² - (4)²)

Use a² - b² = (a - b)(a + b).

= 2(x² - 4)(x² + 4)

Use a² - b² = (a - b)(a + b).

= 2(x - 2)(x + 2)(x² + 4)

(10)

16x² - y² + 4yz - 4z²

= 16x² - (y² - 4yz + 4z²)

Use a² - 2ab + b² = (a - b)².

= 16x² - (y - 2z)²

Use a² - b² = (a - b)(a + b).

= (4x - (y - 2z))(4x + (y - 2z))

= (4x - y + 2z)(4x + y - 2z)