GB-05-05-001 · Expanding three brackets

Expand and simplify $(x+11)(x-10)(x+2)$ .

Expanding triple brackets Booklet p. 3

Method

1) Expand first two brackets using a 2×2 grid and simplify

2) Use a 2×3 grid to multiply the quadratic answer with the third bracket

Worked Example (GB-05-05-001)

① Expand first two brackets using 2×2 grid:

×	$x$	$+11$
$x$	$x^2$	$+11x$
$-10$	$-10x$	$-110$

② Multiply simplified quadratic

(x^2 + 1x - 110)

(x + 2)

using 2×3 grid:

×	$x^2$	$+x$	$-110$
$x$	$x^3$	$+x^2$	$-110x$
$+2$	$+2x^2$	$+2x$	$-220$

NOTE: Watch out for signs especially

- \times - = +

x^{3} + 3x^{2} - 108x - 220