Algebra: Addition & Subtraction Practice 2
This section includes 6 targeted questions to help you strengthen your skills in algebraic addition and subtraction. Work through them to practice the rules, add and subtract terms correctly, and expand expressions with confidence.
Related Lessons:
Practice 2 - Question 1
Simplify, leaving your answers in positive index notation \(\left(2xy^2\right)^3\)
Solution:
For students who have not learned the Law Of Indices:
\[
\begin{align*}
\left(2xy^2\right)^3&=\left(2xy^2\right)\left(2xy^2\right)\left(2xy^2\right)\\
&=8x^3y^6
\end{align*}
\]
For students who have learnt the Law Of Indices:
\[
\begin{align*}
\left(2xy^2\right)^3&=\left(2\right)^3\left(x\right)^3\left(y^2\right)^3\\
&=8x^3y^6
\end{align*}
\]
Practice 2 - Question 2
Expand and simplify \(\left(3p-7q\right)\left(2p+5q\right)\)
Solution:
\(\left(3p-7q\right)\left(2p+5q\right)\)
\(=6p^2+15pq-14pq-35q^2\)
\(=6p^2+pq-35q^2\)
Practice 2 - Question 3
What must be added to \(\left(4x+5y-3\right)\) to get \(\left(11x+9y-13\right)\)?
Solution:
Let what to be added be A:
\(A+\left(4x+5y-3\right)=\left(11x+9y-13\right)\)
\(A=\left(11x+9y-13\right)-\)
\(\left(4x+5y-3\right)\)
\(=11x+9y-13-4x-5y+3\)
\(=7x+4y-10\)
Practice 2 - Question 4
Simplify completely the expression \(-3pq\times\sqrt{36p^2q^4}\)
Solution:
For students who have not learnt the Law Of Indices:
\(-3pq\times\sqrt{36p^2q^4}\)\(=\left(-3pq\right)\sqrt{36}\sqrt{p^2}\sqrt{q^4}\)
\(=\left(-3pq\right)\left(\pm6\right)\left(p^\frac{2}{2}\right)\left(q^\frac{4}{2}\right)\)
\(=\pm18p^2q^3\)
For students who have learned the Law Of Indices:
\(-3pq\times\sqrt{36p^2q^4}\)\(=\left(-3pq\right)\left(36\right)^\frac{1}{2}\left(p^2\right)^\frac{1}{2}\left(q^4\right)^\frac{1}{2}\)
\(=\pm18p^2q^3\)
Practice 2 - Question 5
Expand and simplify \(2\left(3m-4\right)^2\)
Solution:
For students who have not learnt the Perfect Square Identities:
\(2\left(3m-4\right)^2\)\(=2\left(3m-4\right)\left(3m-4\right)\)
\(=2\left[\left(3m\right)\left(3m\right)-\left(3m\right)\left(4\right)\right]\)
\(-\left(4\right)\left(3m\right)+\left(4\right)\left(4\right)\)
\(=2\left[9m^2-24mn+16\right]\)
\(=18m^2-48m+32\)
For students who have learned the Perfect Square Identities:
\({2\left(3m-4\right)}^2\)\(=2\left[\left(3m\right)^2-2\left(3m\right)\left(4\right)+\left(4\right)^2\right]\)\(=2\left[9m^2-24mn+16\right]\)
\(=18m^2-48m+32\)
Practice 2 - Question 6
Simplify completely \(3\left(k-5\right)-3\left[2-4\left(k-3\right)\right]\)
Solution:
When expanding expressions with brackets within brackets, always start with the innermost bracket first, then work your way outward.
Make it a habit to simplify the terms inside the bracket before further expansion. This keeps your working neat, reduces mistakes, and makes the expansion much more manageable.
\(3\left(k-5\right)-3\left[2-4\left(k-3\right)\right]\)
\(=3k-15-3\left[2-4k+12\right]\)
\(=3k-15-3\left[14-4k\right]\)
\(=3k-15-42+12k\)
\(=15k-57\)
Step By Step Full Solution
Learning Maths by simply reading written solutions can be challenging, especially when the reasoning behind each step is not clear. To help you better understand the process, below is the complete solution for Practice 2, with every step clearly shown and explained.