Lesson 4 of 4

Factorising.

About 25 minutes · 5 practice questions

Expanding brackets the other way round: when the areas are known, look for the sides. A common factor, a letter in common, sum and product, and the difference of two squares.

Step 1 of 5 · A common factor

Step 1 of 5

A common factor

Until now we knew the sides and worked out the parts. Factorising goes the other way: you know the parts, and look for sides whose product gives them. The board shows the parts $6x$ ⁠ and $15$ ⁠, and the sides are marked with a question mark. A side shared by both parts must divide both. Predict, then see the sides.

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Step 2 of 5

Finding the factor

Now you build the rectangle: p is the left side, and q is the number in the top side, $x + q$ ⁠. The target is written under the board, and it says when you have reached it.

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Step 3 of 5

A letter in common

A letter can be a common factor too, when it appears in every term. Here the parts are $x^2$ ⁠ and $5x$ ⁠. Predict what the sides are.

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Step 4 of 5

Sum and product

In the previous Lesson we saw that in $(x + p)(x + q)$ ⁠ the middle term is $(p + q)x$ ⁠, and the corner is $p \cdot q$ ⁠. Here you go the other way: choose p and q so that the rectangle gives the target under the board.

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Step 5 of 5

The difference of two squares

Sometimes the two middle parts cancel each other: one pale and one solid, of the same size. Then only the corners are left. Predict which sides the rectangle is made of, then see.

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Interactive scene

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Each step sets up the Scene for you, and a control marked “fixed” stays put for that step.

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