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Multiply out and simplify $(x + 3)(x - 2)$ - Junior Cycle Mathematics - Question 7 - 2019

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Question 7

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Multiply out and simplify $(x + 3)(x - 2)$. Factorise $x^2 - 64$.

Worked Solution & Example Answer:Multiply out and simplify $(x + 3)(x - 2)$ - Junior Cycle Mathematics - Question 7 - 2019

Step 1

Multiply out and simplify $(x + 3)(x - 2)$

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Answer

To multiply out the expression, we can use the distributive property:

  1. Distribute each term in the first bracket to each term in the second bracket:

    (x+3)(x−2)=x(x)+x(−2)+3(x)+3(−2)(x + 3)(x - 2) = x(x) + x(-2) + 3(x) + 3(-2) 2. Simplifying this we have:

    x2−2x+3x−6x^2 - 2x + 3x - 6

    1. Combining like terms:

    x2+x−6x^2 + x - 6

Step 2

Factorise $x^2 - 64$

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Answer

The expression x2−64x^2 - 64 is a difference of squares, which can be factored using the formula:

a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)

In this case:

  • Let a=xa = x and b=8b = 8, since 64=8264 = 8^2.
  • Therefore, we can factor as follows:

x2−64=(x−8)(x+8)x^2 - 64 = (x - 8)(x + 8)

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