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  1. Problems
  2. /Algebra
  3. /Algebraic Identities and Factorisation

Algebraic Identities and Factorisation

Mathematics
+ Upload a Problem
More in AlgebraLinear Equations in Two VariablesPairs of Linear EquationsPolynomialsAlgebraic Identities and FactorisationQuadratic EquationsSequences and SeriesLinear InequalitiesComplex NumbersPermutations and CombinationsBinomial TheoremMatrices and Determinants
10 problems
Type:
1.
Show that if x + y + z = 0, then x³ + y³ + z³ = 3xyz. Use it to find 9³ + (-4)³ + (-5)³.
High School (9–10), General · Algebraic Identities and FactorisationStemPy LabStemPy Lab
Hard
2.
Factorise 27x³ + 64y³.
High School (9–10), General · Algebraic Identities and FactorisationStemPy LabStemPy Lab
Medium
3.
Expand (3x + 2y)² and (x - 3y)³.
High School (9–10), General · Algebraic Identities and FactorisationStemPy LabStemPy Lab
Medium
4.
Use an identity to find each value. 107 × 93; 95²; 101³
High School (9–10), General · Algebraic Identities and FactorisationStemPy LabStemPy Lab
Easy
5.
Factorise x³ + 2x² - 13x + 10.
High School (9–10), General · Algebraic Identities and Factorisation, PolynomialsStemPy LabStemPy Lab
Hard
6.
Factorise 6x² + 11x + 3.
High School (9–10), General · Algebraic Identities and Factorisation, PolynomialsStemPy LabStemPy Lab
Medium
7.
Factorise x² + 9x + 20 and x² - 3x - 28.
High School (9–10), General · Algebraic Identities and Factorisation, PolynomialsStemPy LabStemPy Lab
Easy
8.
Show that x + 3 is a factor of x³ + 4x² + 5x + 6, and find the other factor.
High School (9–10), General · Polynomials, Algebraic Identities and FactorisationStemPy LabStemPy Lab
Medium
9.
Find the value of k for which x - 2 is a factor of kx² - 5x + 2.
High School (9–10), General · Polynomials, Algebraic Identities and FactorisationStemPy LabStemPy Lab
Medium
10.
Use the factor theorem to decide each one.
High School (9–10), General · Polynomials, Algebraic Identities and FactorisationStemPy LabStemPy Lab
Easy