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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

Question 2

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

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Answer

To expand the expression $(x + 5)(x - 9)$ , we apply the distributive property:

First, multiply $x$ by both terms in the second bracket:
- $x \cdot x = x^2$
- $x \cdot (-9) = -9x$
Next, multiply $5$ by both terms in the second bracket:
- $5 \cdot x = 5x$
- $5 \cdot (-9) = -45$
Now, combine these results: $x^2 - 9x + 5x - 45$
Simplify by combining like terms: $x^2 - 4x - 45$

The final expanded and simplified expression is:

$x^2 - 4x - 45$

Step 2

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Answer

To factorise the expression $9x^2 + 6x$ , follow these steps:

Identify the greatest common factor (GCF) of the terms. The GCF of $9x^2$ and $6x$ is $3x$ .
Factor out $3x$ from both terms: $9x^2 + 6x = 3x(3x + 2)$

Thus, the fully factorised form of the expression is:

$3x(3x + 2)$

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