Algebra

Grid expansion

See every part of a product.

Predict, test and explain

Step 1 of 3

Predict

What is (x + 2)(x + 3) after expanding?

(x+2)(x+3)=x2+5x+6(x + 2)(x + 3) = x^2 + 5x + 6
x2x^2
2x2x
3x3x
66
xx
xx
33
22

Scroll the diagram sideways to see every label.

px+qx=5xpx+qx = 5xpq=6pq = 6

InvestigateWhere do the two x terms come from?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Expand and simplify.

(x+4)(x−2)(x+4)(x-2)

Hint

Multiply every term in the first bracket by every term in the second.

Reveal answer

Combine the two linear products after calculating all four products.

(x+4)(x−2)=x2+2x−8(x+4)(x-2)=x^2+2x-8

Build an explanation

Hint 1

Each grid cell combines one term from each bracket.

Hint 2

There are four products; include both x-terms.

Hint 3

Multiply every pair, then collect terms with the same power of x.

Worked example

This example uses fixed values, separate from the diagram controls.

Expand (x + 2)(x + 3).

  1. The four cells give x², 3x, 2x and 6.
  2. Collect 3x + 2x to make 5x.

Answer: x² + 5x + 6.

Connect this idea

Watch out: Multiplying only the first and last terms misses the two middle products.