# Video: AQA GCSE Mathematics Higher Tier Pack 2 β’ Paper 3 β’ Question 18

Expand and simplify (2π₯ β 4)(5π₯Β² + 3) β 3(β2π₯Β³ + π₯).

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### Video Transcript

Expand and simplify two π₯ minus four times five π₯ squared plus three minus three times negative two π₯ cubed plus π₯.

Our first step will be to multiply out all of the brackets. Beginning with the first term, we have two π₯ times five π₯ squared, two π₯ times three. Notice that weβre going to be adding all of these terms that weβre multiplying together. When we move on to negative four times five π₯ squared, weβre adding negative four times five π₯ squared.

It would still be true to say subtracting four times five π₯ squared. However, keeping that negative with its term will prevent us from making sign mistakes later in the problem. Weβll multiply negative four times three. And then we can multiply out negative three times negative two π₯ cubed plus π₯. Iβll use addition and then say negative three times negative two π₯ cubed plus negative three times π₯.

Letβs do some multiplication here. Two π₯ times five π₯ squared equals 10π₯ cubed, plus two π₯ times three, which equals six π₯. Negative four times five π₯ squared equals negative 20π₯ squared. Negative four times three equals negative 12. Negative three times negative two π₯ cubed equals six π₯ cubed. Negative times a negative is a positive. And then negative three times π₯ equals negative three π₯.

In our next step, in order to simplify, we need to combine like terms. Like terms are terms whose variables and their exponents are the same. 10π₯ cubed and six π₯ cubed are like terms. We can add them together. We add them together by adding their coefficients, 10 plus six. And we get 16π₯ cubed. And weβre finished with those two terms.

Now that weβre finished with our π₯ cubed term, weβll look for π₯ squared terms. Thereβs only one negative 20π₯ squared. So now weβll say minus 20π₯ squared. After the π₯ squared term, weβll look for any π₯ terms, π₯ to the first power. And we have six π₯ plus negative three π₯. When we add those together, we get positive three π₯.

Our last term will be any constants. And we only have one, negative 12. So we just bring that down. The expanded and simplified form of this expression is 16π₯ cubed minus 20π₯ squared plus three π₯ minus 12.