Algebra: Addition & Subtraction Practice 1
This section contains 6 focused practice questions designed to strengthen your understanding of algebraic addition and subtraction. Through these questions, you will practise applying the rules for adding and subtracting algebraic terms, as well as expanding expressions correctly
Related Lessons:
Practice 1 - Question 1
Expand and simplify \(-3x\left(2x-5\right)\)
Solution:
\(-3x\left(2x-5\right)\)
\(=\left(-3x\right)\left(2x\right)+\left(-3x\right)\left(-5\right)\)
\(=-6x^2+15x\)
Practice 1 - Question 2
Expand and simplify \(7\left(x-4\right)-3\left(2x+4\right)\)
Solution:
\(7\left(x-4\right)-3\left(2x+4\right)\)
\(=7x-28-6x-12\)
\(=x-40\)
Practice 1 - Question 3
Subtract \(7x-6y\) from the sum of \(12y-4x\) and \(21x-17y\)
Solution:
\(\left(12y-4x\right)+\left(21x-17y\right)-\left(7x-6y\right)\)
\(=12y-4x+21x-17y-7x+6y\)
\(=10x+y\)
Practice 1 - Question 4
Expand and simplify \(-7a\left(-2a+3b\right)\)
Solution:
\(-7a\left(-2a+3b\right)\)
\(=\left(-7a\right)\left(-2a\right)+\left(-7a\right)\left(3b\right)\)
\(=14a^2-21ab\)
Practice 1 - Question 5
Simplify the expression \(5y-2\left(x-2y\right)\)
Solution:
\[
\begin{align*}
5y-2\left(x-2y\right)&=5y-2x+4y\\
&=9y-2x
\end{align*}
\]
Practice 1 - Question 6
Expand and simplify \(\left(3a-7\right)^2-7a\left(2a-9\right)\)
Solution:
For students who have not learned the Perfect Square Identity:
\(\left(3a-7\right)^2-7a\left(2a-9\right)\)\(=\left(3a-7\right)\left(3a-7\right)-7a\left(2a-9\right)\)
\(=\left(3a\right)\left(3a\right)-\left(3a\right)\left(7\right)-\left(7\right)\left(3a\right)\)\(+\left(7\right)\left(7\right)-14a^2+63a\)
\(=9a^2-42a+49-14a^2+63a\)
\(=-5a^2+21a+49\)
For students who have already learned how to apply the Perfect Square Identity:
\(\left(3a-7\right)^2-7a\left(2a-9\right)\)\(=\left(3a\right)^2-2\left(3a\right)\left(7\right)+\)\(\left(7\right)^2-14a^2+63a\)
\(=9a^2-42a+49-14a^2+63a\)
\(=-5a^2+21a+49\)
Step By Step Solution For Q1 to Q6
Below is the step by step solution for the above practice question 1 to 6. Students are encourage to go thru the solutoin as it gives more insights on how the solutions are formulated.