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Example 1;

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$3xy^4 +9xy^2 -6x^2y$

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First check if the equation can be divided across by a constant,

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$3(xy^4 +3xy^2 -2x^2y)$

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Next, check if the equation can be divided across by any term(s)

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$3xy(y^3 +3y -2x)$

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Example 2;

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$9x^2 - 49$

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This is the differnce of 2 squares!!

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Always in the form (x - )(x + )

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Get the square root of both numbers in the equation $\\sqrt9 = 3$ and $\\sqrt49 = 7$

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(3x - 7)(3x + 7)

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Example 3;

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$2ab - 6ac - bd + 3cd$

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Gather the terms that has common factors and take them out, similar as part 1

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$2a(b - 3c) - d(b - 3c)$

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Next, since there is a common factor bracket, the equation can be reduced further

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$(b - 3c)(2a - d)$

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(i)  $\\simplify{{num12[0]} *{ num11[0]}}xy - \\simplify{{num12[0]}*{num11[1]}}xw + \\simplify{{num12[0]}*{num11[2]}}xz$

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[[0]]

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(ii)  $\\simplify{{num12[1]} *{ num11[3]}}xy^4 + \\simplify{{num12[1]}*{num11[4]}}xy^2 - \\simplify{{num12[1]}*{num11[5]}}x^2y$

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[[1]]

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(iii)  $\\simplify{{num12[2]} *{ num11[6]}}x^2 - \\simplify{{num12[2]}*{num11[7]}}xy + \\simplify{{num12[2]}*{num11[8]}}x^3$

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[[2]]

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(i)  $\\simplify{{num22[0]} *{ num22[0]}}x^2 - \\simplify{{num22[3]}*{num22[3]}}$

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[[0]]

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(ii)  $\\simplify{{num22[1]} *{ num22[1]}}x^2 - \\simplify{{num22[4]}*{num22[4]}}$

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[[1]]

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(iii)  $\\simplify{{num22[2]} *{ num22[2]}}x^2 - \\simplify{{num22[5]}*{num22[5]}}$

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[[2]]

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(i)  $\\simplify{{num32[0]} *{ num32[1]}}ab - \\simplify{{num32[0]}*{num32[3]}}ac - \\simplify{{num32[2]}*{num32[1]}}bd + \\simplify{{num32[2]}*{num32[3]}}cd$

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[[0]]

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(ii)  $\\simplify{{num32[4]} *{ num32[5]}}a^2 + \\simplify{{num32[4]}*{num32[7]}}a + \\simplify{{num32[6]}*{num32[5]}}a + \\simplify{{num32[6]}*{num32[7]}}$

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[[1]]

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(iii)  $\\simplify{{num32[8]} *{ num32[9]}}xy - \\simplify{{num32[8]}*{num32[5]}}x^2y - \\simplify{{num32[3]}*{num32[5]}}x + \\simplify{{num32[3]}*{num32[9]}}$

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[[2]]

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Factorise each of the following:

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Factorising algebraic expressions

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rebelmaths

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