🔢 Expanding Double Brackets

About Expanding Double Brackets

Expanding a double bracket means multiplying every term in the first by every term in the second, and the single most common error is missing one of the four products. A grid makes that error structurally difficult: two terms head the rows, two head the columns, and the four empty cells are visibly waiting to be filled. A pupil who leaves one blank can see that they have. This worksheet prints that grid for every question, with a ruled line beneath for the simplified expression once the like terms have been collected. The expansion behind each question is done on polynomials held as coefficients by degree, so the four cross-products, the simplified answer and the answer key all come from one calculation — a missing or duplicated product is not something the generator can produce. The levels bring in structure in order: positive terms first, then larger constants, then a single negative term, then mixed signs where two negatives multiply to a positive, and finally coefficients on both x terms so the leading coefficient is no longer one. Four grids per page with room to work. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key. Its on-screen twin is Expand Distribute Escape.

Common questions

Why use a grid rather than FOIL?

The four empty cells make a missing product visible. A pupil who leaves one blank can see that they have.

Can a cross-product be missing from the grid?

No. The grid is always exactly two by two, drawn from the same expansion that produces the key.

When do negative terms appear?

From the third level — one negative first, then mixed signs where two negatives multiply to a positive.

How many grids are on a page?

Four, each with a ruled line for the simplified expression.