Algebraic Identities Practice Questions with Detailed Solutions – Level 1

Algebraic Identities Practice Quiz Level 1: Squares, Cubes and Sums

This is Level 1 of the Algebraic Identities practice set on Aptitude360, covering the standard square, cube and three-variable identities used in quantitative aptitude. Questions ask you to find unknown expressions from given sums and products, calculate large squares and cubes quickly, and simplify decimal fractions, with a worked solution for each.

Topics covered in this Algebraic Identities set

• Sum of squares and square of a difference from a given sum and product
• Difference of squares for fast mental calculation
• Squares and cubes of numbers close to a hundred or a thousand
• Expressions in a variable and its reciprocal, up to cubes
• Square of a trinomial and coefficients in its expansion
• Sum of three cubes minus three times their product, including the case when the sum is zero
• Simplifying decimal fractions with sum and difference of cubes, and factorising a sum of cubes

Key algebraic identity formulas for Level 1

• Square of a sum: \( (a+b)^{2}=a^{2}+2ab+b^{2} \)
• Difference of squares: \( a^{2}-b^{2}=(a+b)(a-b) \)
• Sum of cubes: \( a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}) \)
• Trinomial square: \( (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca) \)
• Reciprocal square: \( x^{2}+\dfrac{1}{x^{2}}=\left(x+\dfrac{1}{x}\right)^{2}-2 \)
• If \( a+b+c=0 \): \( a^{3}+b^{3}+c^{3}=3abc \)

Revision tips for algebraic identities

• Write a number near a round base as the base plus or minus a small value before squaring or cubing.
• When three values add up to zero, use the sum-of-cubes shortcut instead of cubing each one.
• Spot the sum or difference of cubes pattern in decimal fractions; the expression usually cancels to a simple sum or difference.

Who should take Algebraic Identities Level 1

Students starting quantitative aptitude for SSC, banking or management entrance exams who need a firm grip on the basic identities.