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Factorisation –

[tex]1) \: \: \tt \: {x}^{2} – {4y}^{2} [/tex]
[tex]2) \: \: \tt \: {9a}^{2} {x}^{2} – 9

By Quinn

Factorisation –

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

Please solve the above.
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About the author
Quinn

Imagine that you are the boy who rescued the duck. Write your experience how

you shot the duck and how it changed the

write the formula to find sum of the first even natural number​

2 thoughts on “Factorisation –<br /><br />[tex]1) \: \: \tt \: {x}^{2} – {4y}^{2} [/tex]<br />[tex]2) \: \: \tt \: {9a}^{2} {x}^{2} – 9”

  1. 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)

    Reply

  2. Answer:

    Factorisation –

    [tex]1) \: \: \tt \: {x}^{2} – {4y}^{2} [/tex]

    [tex]2) \: \: \tt \: {9a}^{2} {x}^{2} – 9 {b}^{3} [/tex]

    [tex]3) \: \: \tt \: \frac{ {a}^{2} }{9} – \frac{ {b}^{4} }{16} [/tex]

    [tex]4) \: \: \tt \: {48x}^{3} – 27x[/tex]

    [tex]5) \: \: \tt \: 4 {a}^{2} b – 9 {b}^{3} [/tex]

    [tex]6) \: \: \tt \: {a}^{2} – 81(b – c) ^{2} [/tex]

    [tex]7) \: \: \tt \: {a}^{4} – 1[/tex]

    [tex]8) \: \: \tt \: {9a}^{2} – ( {a}^{2} – 4) ^{2} [/tex]

    [tex]9) \: \: \tt \: 2 {x}^{4} – 32[/tex]

    [tex]10) \: \: \tt \: {16x}^{2} – {y}^{2} + 4yz – {4z}^{2} [/tex]

    Please solve the above. not simple please brainliest answers

    Reply

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