Expanding binomial products

Expanding (a + b)(c + d) with FOIL or an area diagram, perfect squares and the difference of two squares.

Two brackets

Multiply each term in the first bracket by each term in the second: $(a + b)(c + d) = ac + ad + bc + bd$.

Same graph, two forms

The bracket form and the expanded form give exactly the same graph, so they are equal for every x.

Example 1●

Expand $(2x - 1)(x + 4)$.

$2x^2 + 8x - x - 4$

$= 2x^2 + 7x - 4$

Example 2●●

Expand $(3x - 2)^2$ and $(x - 5)(x + 5)$.

$(3x)^2 - 2(3x)(2) + 2^2 = 9x^2 - 12x + 4$

$x^2 - 25$ (the middle terms cancel)

Flashcards

$(x + 3)(x + 5)$

$x^2 + 8x + 15$

$(x + 4)^2$

$x^2 + 8x + 16$

$(x - 7)(x + 7)$

$x^2 - 49$

Practice

Expand $(2x - 1)(x + 4)$.
Expand $(3x - 2)^2$.
Expand $(x - 5)(x + 5)$.
Expand $(x + 3)(x + 5)$.
Expand $(x + 4)^2$.
Expand $(x - 4)(x + 3)$.
Expand $(2a + 3)(2a - 3)$.
Expand $(2x + 3)(3x - 5)$.