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Question 8 a) Multiply out and simplify $(x + 9)(2x - 1)$ - Junior Cycle Mathematics - Question 8 - 2016

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Question 8

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Question 8 a) Multiply out and simplify $(x + 9)(2x - 1)$. b) Factorise fully $3ax + ay + 3cx + cy.$

Worked Solution & Example Answer:Question 8 a) Multiply out and simplify $(x + 9)(2x - 1)$ - Junior Cycle Mathematics - Question 8 - 2016

Step 1

Multiply out and simplify $(x + 9)(2x - 1)$

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Answer

To multiply out the expression, use the distributive property (also known as the FOIL method for binomials):

  1. First, multiply xx by both terms in (2x−1)(2x - 1):

    x⋅2x−x⋅1=2x2−xx \cdot 2x - x \cdot 1 = 2x^2 - x

  2. Next, multiply 99 by both terms in (2x−1)(2x - 1):

    9⋅2x−9⋅1=18x−99 \cdot 2x - 9 \cdot 1 = 18x - 9

  3. Combine all the terms:

    2x2−x+18x−92x^2 - x + 18x - 9

  4. Now, simplify by combining like terms:

    2x2+17x−92x^2 + 17x - 9

Step 2

Factorise fully $3ax + ay + 3cx + cy$

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Answer

To factorise the expression, first group the terms that have common factors:

  1. Group the terms:

    (3ax+3cx)+(ay+cy)(3ax + 3cx) + (ay + cy)

  2. Factor out the common factors in each group:

    3x(a+c)+y(a+c)3x(a + c) + y(a + c)

  3. Now, factor out the common binomial factor (a+c)(a + c):

    (a+c)(3x+y)(a + c)(3x + y)

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