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(a) Multiply out and simplify $(x + 3)(x - 2).$ (b) Factorise $x^2 - 64.$ - Junior Cycle Mathematics - Question 7 - 2019

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(a)-Multiply-out-and-simplify---$(x-+-3)(x---2).$----(b)-Factorise-$x^2---64.$-Junior Cycle Mathematics-Question 7-2019.png

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

Worked Solution & Example Answer:(a) Multiply out and simplify $(x + 3)(x - 2).$ (b) Factorise $x^2 - 64.$ - 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, use the distributive property:

(x+3)(x−2)=x(x−2)+3(x−2)(x + 3)(x - 2) = x(x - 2) + 3(x - 2)

Expanding both terms:

=x2−2x+3x−6= x^2 - 2x + 3x - 6

Now combine like terms:

=x2+x−6.= x^2 + x - 6.

Thus, the simplified form is:

x2+x−6.x^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, we have:

a=xandb=8a = x \quad \text{and} \quad b = 8

Thus, we can factor as follows:

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

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