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So using the strategy to determine the area of the large rectangle I simply did

$10\times10, 10\times2, 10\times4, 2\times4$ to get $168\mathrm{cm}$ total.

The next question goes on to ask how this strategy relates to binomial multiplication.

$14\times12 = 10\times10 + 10\times2 + 10\times4 + 2\times4$

I'm confused as to how this question relates to binomial multiplication because it doesn't look like it can be put in a for such as $(5x+2)(3x-1)$.

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Take your second diagram and replace $10$ cm and $2$ cm along the top with $5x$ and $2$, respectively, and similarly replace $10$ cm and $4$ cm on the side with $3x$ and $-1$. Now, this is a little strange since $-1$ is negative, but the principle remains the same.

The total area of the rectangle is $(5x+2)(3x-1)$, which you can see as the area of four smaller rectangles $5x \cdot 3x$, etc.

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HINT: Start with this...

$10 \times 10 + 10 \times 2 = 10(10 + 2)$

Do the same for the other two terms $10 \times 4 + 2 \times 4$ (pull out common factor). You should then have a common binomial to factor out leading to 2 binomials multiplied together.

You may be expecting to see a variable like $x$ (based on your last sentence) in your binomials but you won't in this case. Should just have numbers in each binomial.

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Binomial multiplication is really anything that can be written in the form $(a+b)\times(c+d)$. We already know that the area of the rectangle is given by $12\times14$, so you just need to split $12$ into the right $a$ and $b$ and split $14$ into the right $c$ and $d$.

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