Expanding single and double brackets

Task goals

• Expand a single bracket with a positive or negative multiplier, e.g. $4(x+3)$ or $-3(y-5)$.
• Expand a single bracket and collect an outside like term, e.g. $3(x+2)+4x$ or $6(x-2)-3x$.
• Expand a single bracket with a coefficient inside, e.g. $2(3x+5)$ or $4(2x-3)$.
• Expand and collect two separate single-bracket terms, e.g. $2(x+5)+3(x+1)$.
• Use single-bracket expansion in a context problem, e.g. writing the area of a rectangle with one algebraic side as an expanded expression.
• Name the number property (distributive) that justifies a single-bracket expansion.
• Expand two linear brackets using FOIL, e.g. $(x+4)(x+3)$ or $(x-4)(x-2)$, including a leading coefficient greater than $1$, e.g. $(2x+1)(x+3)$.
• Use double-bracket expansion in a context problem, e.g. writing the area of a rectangle with two algebraic sides as an expanded expression.
• Expand a double bracket and collect an extra outside like term, e.g. $(x+3)(x+2)+4x$.
• Find a missing term in a bracket given the expanded trinomial, e.g. $(x+\square)(x+3)=x^2+7x+12$.
• Expand a perfect square, e.g. $(x-6)^2$ or $(3x-2)^2$, and explain a common error such as $(x-6)^2=x^2+36$.
• Expand a difference-of-squares product, e.g. $(x+7)(x-7)$ or $(2x-3)(2x+3)$, and find a missing value that makes a stated identity true.
• Expand and simplify an expression combining two double-bracket expansions, e.g. $(x+4)(x-2)-(x-3)(x+1)$ or $(2x+1)^2-(x-3)(x+3)$.