Adding and Subtracting Expressions (Like Terms)

Task goals

• Collect straightforward like terms with signed integer coefficients, e.g. $5x+3x$ or $4y+2y-y$.
• Collect like terms across two variables and constants in the same expression, e.g. $3x+4y+2x-y$ or $5m+7-2m+3$.
• Name the number property shown by a given identity, e.g. $a+b=b+a$ (commutative) or $a(b+c)=ab+ac$ (distributive), and state the additive or multiplicative identity/inverse.
• Distribute a single bracket by a positive or negative numeric factor and collect the resulting like terms, e.g. $3(x+4)+2x$ or $5(2b+1)-3b$.
• Distribute and collect across two brackets, including a subtracted bracket where every sign inside flips, e.g. $4(a-1)+2(a+3)$ or $3(x+2)-(x-4)$.
• Collect like surds, recognising that only terms with the same number under the root can combine, e.g. $2\sqrt3+5\sqrt3$ or $3\sqrt2+4-\sqrt2+1$.
• Simplify an expression mixing a distributed bracket with a surd term, e.g. $2(x+3\sqrt2)-(x-\sqrt2)$.
• Use simplifying in a context problem such as finding the perimeter of a rectangle or triangle with algebraic and surd side lengths.
• Solve a "find $k$" problem where a missing coefficient makes a stated simplification true, e.g. $6x+kx=17x$.
• Identify and explain an error in an incorrect simplification, such as wrongly combining unlike surds.