Expanding double brackets

Task goals

• Expand a pair of binomial brackets of the form $(x+a)(x+b)$ where both constants are positive, using the distributive property.
• Expand a pair of binomial brackets with mixed signs, such as $(x+a)(x-b)$, including where one bracket has a leading coefficient greater than 1.
• Fill in a missing constant term in a partially-expanded identity, such as $(x+3)(x+4)=x^2+7x+\square$.
• Expand a pair of binomial brackets where both brackets have a leading coefficient greater than 1, such as $(2x+1)(3x+2)$.
• Expand a perfect-square or difference-of-squares expression, such as $(x+a)^2$ or $(x-a)(x+a)$.
• Expand and simplify an expression that combines a double-bracket expansion with an extra term, such as $(x+2)(x+3)+5$.
• Judge whether a given expanded statement is true or false, or use an area model (rectangle side lengths) to represent and check a binomial expansion.