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1 (a) Expand and simplify \( (x + 5)(x - 9) \) (b) Factorise fully \( 9x^2 + 6x \) - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

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1-(a)-Expand-and-simplify--\(-(x-+-5)(x---9)-\)--(b)-Factorise-fully-\(-9x^2-+-6x-\)-Edexcel-GCSE Maths-Question 2-2019-Paper 3.png

1 (a) Expand and simplify \( (x + 5)(x - 9) \) (b) Factorise fully \( 9x^2 + 6x \)

Worked Solution & Example Answer:1 (a) Expand and simplify \( (x + 5)(x - 9) \) (b) Factorise fully \( 9x^2 + 6x \) - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 3

Step 1

Expand and simplify \( (x + 5)(x - 9) \)

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Answer

To expand the expression, we use the distributive property (FOIL method).

  1. Multiply the first terms: ( x \cdot x = x^2 )
  2. Multiply the outer terms: ( x \cdot (-9) = -9x )
  3. Multiply the inner terms: ( 5 \cdot x = 5x )
  4. Multiply the last terms: ( 5 \cdot (-9) = -45 )

Now combine the like terms:

[ x^2 - 9x + 5x - 45 = x^2 - 4x - 45 ]

Thus, the simplified expression is ( x^2 - 4x - 45 ).

Step 2

Factorise fully \( 9x^2 + 6x \)

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Answer

To factorise the expression ( 9x^2 + 6x ), we start by identifying the common factors:

  1. The common factor in both terms is ( 3x ).
  2. Factor out ( 3x ): [ 9x^2 + 6x = 3x(3x + 2) ]

Hence, the fully factorised form is ( 3x(3x + 2) ).

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