alleryIf $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?
- $14$
- $10$
- $21$
- $28$
Show answer and solution
Correct answer: C. $21$
Use the difference-of-squares identity $a^2 - b^2 = (a+b)(a-b) = 7 \times 3 = 21$.
AFCAT Elementary Algebra — practice questions
Explore 6 free Elementary Algebra questions in AFCAT Quantitative Reasoning. Open each question or exercise to read its content, reference answers and available explanation.
Practise Elementary Algebra with Quill →Elementary Algebra questions and exercises with answers
Showing questions 1–6 of 6.
If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?Read the answer and worked solution →Expand $(x + 5)^2$.Read the answer and worked solution →If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?Read the answer and worked solution →Factorise $a^3 - b^3$.Read the answer and worked solution →If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.Read the answer and worked solution →If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 14$, find $ab + bc + ca$.Read the answer and worked solution →
Worked practice questions
Expand $(x + 5)^2$.
- $x^2 + 10x + 10$
- $x^2 + 5x + 25$
- $x^2 + 25$
- $x^2 + 10x + 25$
Show answer and solution
Correct answer: D. $x^2 + 10x + 25$
$(a+b)^2 = a^2 + 2ab + b^2$.
With $a=x, b=5$: $x^2 + 10x + 25$.
If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?
- $3abc$
- $-3abc$
- $0$
- $abc$
Show answer and solution
Correct answer: A. $3abc$
The identity $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ has right-hand side zero when $a+b+c=0$. Therefore $a^3+b^3+c^3=3abc$, so option A is correct. The sum being zero does not by itself imply that the sum of cubes is zero.
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