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Class 9 Exploring Algebraic Identities worksheet
CBSE Mathematics. (a ± b)³, (a + b + c)², sums and differences of cubes, a³ + b³ + c³ − 3abc, factorising. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
(x + 6)³ expands to:
- x³ + 18x² + 18x + 216
- x³ + 216
- x³ + 6x² + 36x + 216
- x³ + 18x² + 108x + 216
Answer
(d) x³ + 18x² + 108x + 216
a = x, b = 6: a³ + 3a²b + 3ab² + b³
- 2.
(3x − 9)³ expands to:
- 27x³ − 243x² + 729x − 729
- 27x³ − 729
- 27x³ + 243x² − 729x − 729
- 27x³ − 243x² − 729x − 729
Answer
(a) 27x³ − 243x² + 729x − 729
a = 3x, b = 9: a³ − 3a²b + 3ab² − b³
- 3.
(a + b)³ equals:
- a³ + 3a²b + b³
- a³ + 3ab + b³
- a³ + 3a²b + 3ab² + b³
- a³ + b³
Answer
(c) a³ + 3a²b + 3ab² + b³
Section B · short answer
- 4.
Expand (x + 6y + 3z)².
Answer
x² + 36y² + 9z² + 12xy + 36yz + 6zx
a² + b² + c² + 2ab + 2bc + 2ca
- 5.
Expand (3x − 4)³.
Answer
27x³ − 108x² + 144x − 64
(3x)³ − 3(3x)²(4) + 3(3x)(4)² − 4³
Section C · long answer
- 6.
A cube of side (x + 5) cm is built from small cubes of side 1 cm. Write its volume as an expanded polynomial, then find the volume when x = 17.
Answer
x³ + 15x² + 75x + 125; 10648 cm³
(x + 5)³; 22³ = 10648
Fresh sheets for your child
In the app, every Exploring Algebraic Identities sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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