What is the factorised form of (x^2+10x+25)?
Correct answer: A
This is a perfect square trinomial because (25=5^2) and (10x=2\cdot5\cdot x). Exam tip: identify the perfect square first.
View question detailsMathematics
Factorisation
गुणनखंडन
Factorisation is a Class 9 Mathematics topic within the chapter “Exploring Algebraic Identities.” Students learn how to rewrite algebraic expressions as products of simpler factors by taking out common factors, grouping terms, and applying identities such as the difference of squares and perfect-square forms. They practise recognising patterns, checking results by expansion, and using factorisation to simplify expressions and solve related algebraic problems accurately.
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Expert · Level 71 · factorisation,perfect square,algebraic identities
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- ((x+5)^2)
- ((x-5)^2)
- ((x+10)(x+25))
- ((x+1)(x+25))
Expert · Level 71 · difference of squares,factorisation,identities
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- ((9a-25b)(9a+25b))
- ((3a-5b)(3a+5b))
- ((3a-5b)^2)
- ((9a-5b)(a+25b))
Expert · Level 71 · quadratic factorisation,middle term,school exam
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- ((x+2)(x+6))
- ((x+3)(x+4))
- ((x-3)(x-4))
- ((x+1)(x+12))
Expert · Level 71 · perfect square trinomial,factorisation,class 9
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- ((2p+3q)^2)
- ((4p+9q)^2)
- ((2p-3q)^2)
- ((p+q)(4p+9q))
Expert · Level 71 · quadratic factorisation,negative middle term,factors
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- ((y-5)(y-6))
- ((y+5)(y+6))
- ((y-3)(y-10))
- ((y+1)(y-30))
Expert · Level 71 · perfect square,negative sign,factorisation
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- ((4m+5n)^2)
- ((4m-5n)^2)
- ((16m-25n)^2)
- ((4m-25n)(4m+n))
Expert · Level 71 · difference of cubes,factorisation,identity
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- ((a-b)(a^2+ab+b^2))
- ((a+b)(a^2-ab+b^2))
- ((a-b)(a^2-ab+b^2))
- ((a-b)^3)
Expert · Level 71 · sum of cubes,factorisation,algebraic identity
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- ((a-b)(a^2+ab+b^2))
- ((a+b)(a^2-ab+b^2))
- ((a+b)(a^2+ab+b^2))
- ((a+b)^3)
Expert · Level 71 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, binomial square
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- \(4p^2-20pq+25q^2\)
- \(4p^2-10pq+25q^2\)
- \(4p^2+20pq-25q^2\)
- \(4p^2-20pq+20q^2\)
Expert · Level 71 · factorisation, algebraic identities, perfect square trinomial, quadratic expressions, class 9 mathematics
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- \(9x^2-12x+4\)
- \(9x^2-12x+5\)
- \(9x^2-10x+4\)
- \(9x^2-12x-4\)
Expert · Level 71 · advanced factorisation,middle term,splitting
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- ((3a-2b)(4a-3b))
- ((6a-b)(2a-6b))
- ((12a-6b)(a-b))
- ((3a+2b)(4a+3b))
Expert · Level 71 · factorisation by grouping,common bracket,algebra
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- ((x+5)(2y+3))
- ((2x+5)(y+3))
- ((2x+3)(y+5))
- ((x+3)(2y+5))
Expert · Level 71 · combined identities,perfect square,difference of squares
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- ((a+b-c)(a+b+c))
- ((a-b-c)(a-b+c))
- ((a+b)^2-c)
- ((a+c)(b-c))
Expert · Level 71 · perfect square trinomial,factorisation,negative middle term
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- ((5x+3y)^2)
- ((25x-9y)^2)
- ((5x-3y)^2)
- ((5x-9y)(5x+y))
Expert · Level 71 · sum of cubes,cubic factorisation,class 9
View options
- ((x+2)(x^2-2x+4))
- ((x-2)(x^2+2x+4))
- ((x+2)(x^2+2x+4))
- ((x+2)^3)
Expert · Level 71 · algebraic identities, factorisation, sum of cubes, class 9 mathematics, cubes
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- \(x^3+8\)
- \(x^2+8\)
- \(x^3-8\)
- \(x^2-8\)
Expert · Level 71 · common factor,difference of squares,complete factorisation
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- (5(x^2-4))
- (5(x-2)(x+2))
- ((5x-20)(x+1))
- (5(x-2)^2)
Expert · Level 71 · common factor,algebraic factorisation,monomials
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- (3ab(a+2b-3))
- (3a(a+2b-3))
- (ab(3a+6b-9ab))
- (3b(a^2+2b-3))
Expert · Level 71 · combined factorisation,perfect square,difference of squares
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- ((x+y-z)(x+y+z))
- ((x-y-z)(x-y+z))
- ((x+y)^2-z^2)
- ((x+z)(y-z))
Expert · Level 71 · algebraic identities, factorisation, perfect square trinomial, binomial square, class 9 mathematics
View options
- \(9a^2+12ab+4b^2\)
- \(9a^2+12ab+2b^2\)
- \(9a^2+6ab+4b^2\)
- \(9a^2+12ab-4b^2\)
Write (9a^2-25b^2) in factors.
Correct answer: B
This is a difference of squares where (9a^2=(3a)^2) and (25b^2=(5b)^2). Exam tip: take square roots of both terms.
View question detailsWhich are the correct factors of (x^2+7x+12)?
Correct answer: B
Since (3+4=7) and (3\cdot4=12), the correct factors are ((x+3)(x+4)). Exam tip: match both sum and product.
View question detailsWhat is the factorised form of (4p^2+12pq+9q^2)?
Correct answer: A
The first and last terms are perfect squares and the middle term is (2\cdot2p\cdot3q). Exam tip: confirm with the (2ab) term.
View question detailsWhat do we get by factorising (y^2-11y+30)?
Correct answer: A
Here (-5-6=-11) and ((-5)(-6)=30). Exam tip: for a negative middle term, both factors may be negative.
View question detailsChoose the correct factorised form of (16m^2-40mn+25n^2).
Correct answer: B
The middle term is negative, so the perfect square is ((4m-5n)^2). Exam tip: check both square roots and sign.
View question detailsWhat is the factorised form of (a^3-b^3)?
Correct answer: A
The formula for difference of cubes is (a^3-b^3=(a-b)(a^2+ab+b^2)). Exam tip: keep all signs positive in the second bracket.
View question detailsWhat will be the factorised form of (a^3+b^3)?
Correct answer: B
In sum of cubes, the first factor is ((a+b)) and the second is (a^2-ab+b^2). Exam tip: remember the negative middle sign.
View question detailsWhich of the following trinomials can be factorised as the product of two identical binomials because it is a perfect square?
Correct answer: A
In option A, the first and last terms are \((2p)^2\) and \((5q)^2\). Its middle term is \(-2(2p)(5q)=-20pq\), so it equals \((2p-5q)^2\). Option B has an incorrect middle-term coefficient. Exam tip: for a perfect square trinomial, always check whether the middle term is \(\pm2ab\).
View question detailsWhich of the following quadratic expressions can be written as the square of a single linear binomial?
Correct answer: A
For option A, \(b^2=(-12)^2=144\) and \(4ac=4\times9\times4=144\), so it has equal linear factors: \((3x-2)^2\). Option B fails this test. Exam tip: check \(b^2=4ac\) for a perfect-square trinomial.
View question detailsWhat is the factorised form of (12a^2-17ab+6b^2)?
Correct answer: A
The terms (-9ab) and (-8ab) combine to (-17ab). Exam tip: use product (72a^2b^2) to find the right split.
View question detailsFactorise (2xy+6x+5y+15) by grouping.
Correct answer: B
Grouping gives (2x(y+3)+5(y+3)), so the factor is ((2x+5)(y+3)). Exam tip: look for a common bracket.
View question detailsWhich is the correct factorised form of (a^2+2ab+b^2-c^2)?
Correct answer: A
First take (a^2+2ab+b^2=(a+b)^2), then apply difference of squares. Exam tip: apply combined identities stepwise.
View question detailsFactorise (25x^2-30xy+9y^2).
Correct answer: C
It is ((5x)^2-2\cdot5x\cdot3y+(3y)^2). Exam tip: use the subtraction square for a negative middle term.
View question detailsWhat do we get by factorising (x^3+8)?
Correct answer: A
This is (x^3+2^3), so use the sum of cubes formula. Exam tip: keep the middle term negative in the second bracket.
View question detailsWhich of the following expressions can be factorised using the identity for the sum of two cubes?
Correct answer: A
\(x^3+8=x^3+2^3\), so it is a sum of two cubes and \(a^3+b^3=(a+b)(a^2-ab+b^2)\) applies. \(x^3-8\) is a difference of cubes. Exam tip: recognise \(8=2^3\).
View question detailsWhich is the complete factorised form of (5x^2-20)?
Correct answer: B
First take common factor (5), then factor (x^2-4). Exam tip: apply identities after taking the common factor.
View question detailsWhat is the correct factorised form of (3a^2b+6ab^2-9ab)?
Correct answer: A
The common factor in all three terms is (3ab). Exam tip: take out the greatest common factor.
View question detailsWhat is the factorised form of (x^2+2xy+y^2-z^2)?
Correct answer: A
First (x^2+2xy+y^2=(x+y)^2). Exam tip: use difference of squares after forming the perfect square.
View question detailsWhich of the following expressions is a perfect-square trinomial that can be written as the product of two identical binomials?
Correct answer: A
\(9a^2=(3a)^2\) and \(4b^2=(2b)^2\). For a perfect-square trinomial, the middle term must be \(2\times 3a\times 2b=12ab\). Hence, \(9a^2+12ab+4b^2=(3a+2b)^2=(3a+2b)(3a+2b)\). In option B, the last term is not \(4b^2\), while option C does not have the required middle term \(12ab\). Exam tip: take the square roots of the first and last terms, then check the middle term using \(2pq\).
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