Question

match each expression to its equivalent form.
drag the tiles to the correct boxes to complete the pairs.
tiles
$(x + 4)(x - 4)$ $(x + 2y)(x^2 - 2xy + 4y^2)$ $4x^2 + 12xy + 9y^2$
$8x^3 + 12x^2 + 6x + 1$
pairs
$x^2 - 16$ $\longrightarrow$
$(2x + 1)^3$ $\longrightarrow$
$(2x + 3y)^2$ $\longrightarrow$

Explanation:

Step1: Factor difference of squares

$x^2 - 16 = (x+4)(x-4)$

Step2: Expand cube of binomial

$(2x+1)^3 = 8x^3+12x^2+6x+1$

Step3: Expand square of binomial

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

Step4: Note remaining tile identity

$(x+2y)(x^2-2xy+4y^2) = x^3+8y^3$ (unmatched here)

Answer:

$x^2 - 16 \longrightarrow (x + 4)(x - 4)$
$(2x + 1)^3 \longrightarrow 8x^3 + 12x^2 + 6x + 1$
$(2x + 3y)^2 \longrightarrow 4x^2 + 12xy + 9y^2$