Choose the factorised form of (r^2+4rs+4s^2-9).
Correct answer: A
First write (r^2+4rs+4s^2) as ((r+2s)^2). Exam tip: apply difference of squares after forming a perfect square.
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Factorisation
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Medium · Level 70 · mixed identity,perfect square,factorisation
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- ( (r+2s-3)(r+2s+3) )
- ( (r-2s-3)(r-2s+3) )
- ( (r+4s-9)(r+s+1) )
- ( (r+2s+3)^2 )
Medium · Level 70 · grouping,common binomial,factorisation
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- ( (x+4)(y-2) )
- ( (x-4)(y+2) )
- ( (x+2)(y-4) )
- ( (x-8)(y+1) )
Medium · Level 70 · difference of squares,binomial,factorisation
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- ( (6a-b)(6a+b) )
- ( (36a-b)(a+b) )
- ( (6a+b)^2 )
- ( (6a-b)^2 )
Medium · Level 70 · quadratic,factorisation,signs
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- ( (k-7)(k-8) )
- ( (k+7)(k+8) )
- ( (k-4)(k-14) )
- ( (k-1)(k-56) )
Medium · Level 70 · mixed identity,difference of squares,factorisation
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- ( (x-y+1)(x+y-1) )
- ( (x+y+1)(x-y-1) )
- ( (x-y-1)(x+y+1) )
- ( (x+y-1)^2 )
Medium · Level 70 · quadratic,ac method,factorisation
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- ( (2x+1)(x+3) )
- ( (2x+3)(x+1) )
- ( (x+2)(2x+3) )
- ( (2x-1)(x-3) )
Medium · Level 70 · quadratic,factorisation,grouping
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- ( (3x+4)(x+2) )
- ( (3x+2)(x+4) )
- ( (x+4)(x+6) )
- ( (3x-4)(x-2) )
Medium · Level 70 · common factor,difference of squares,factorisation
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- (3(2a-3b)(2a+3b))
- ( (12a-27b)(a+b) )
- (3(4a^2-9b^2))
- ( (6a-9b)(2a+3b) )
Medium · Level 70 · mixed identity,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^2 )
- ( (a+c-b)(a+c+b) )
Medium · Level 70 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, quadratic expressions
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- \(x^2+10x+25\)
- \(x^2+10x+24\)
- \(x^2+8x+25\)
- \(x^2-10x+24\)
Medium · Level 70 · grouping,common binomial,factorisation
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- ( (3p+2)(2q+3) )
- ( (6p+4)(q+3) )
- ( (3p+4)(2q+6) )
- ( (2p+3)(3q+2) )
Medium · Level 70 · sum of cubes,factorisation,identity
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- ( (4m+5n)(16m^2-20mn+25n^2) )
- ( (4m-5n)(16m^2+20mn+25n^2) )
- ( (4m+5n)(16m^2+20mn+25n^2) )
- ( (64m+125n)(m^2-mn+n^2) )
Medium · Level 70 · difference of cubes,factorisation,identity
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- ( (5x-6y)(25x^2+30xy+36y^2) )
- ( (5x+6y)(25x^2-30xy+36y^2) )
- ( (5x-6y)(25x^2-30xy+36y^2) )
- ( (125x-216y)(x^2+xy+y^2) )
Medium · Level 70 · quadratic,ac method,factorisation
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- ( (2a-5)(a-3) )
- ( (2a-3)(a-5) )
- ( (a-5)(a-6) )
- ( (2a+5)(a+3) )
Medium · Level 70 · quadratic,factorisation,verification
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- ( (3y+1)(y-5) )
- ( (3y-1)(y+5) )
- ( (y-15)(3y+1) )
- ( (3y-5)(y+1) )
Medium · Level 70 · mixed identity,perfect square,difference of squares
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- ( (3x+y-1)(3x+y+1) )
- ( (3x-y-1)(3x-y+1) )
- ( (9x+y-1)(x+y+1) )
- ( (3x+y+1)^2 )
Medium · Level 70 · common factor,factorisation,monomial
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- (5x(3x-4y))
- (5(3x^2-4xy))
- (x(15x-20y))
- (10x(2x-2y))
Medium · Level 70 · quadratic,factorisation,sign choice
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- ( (x+8)(x-3) )
- ( (x-8)(x+3) )
- ( (x+6)(x-4) )
- ( (x+12)(x-2) )
Medium · Level 70 · difference of squares,grouping,factorisation
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- ( (a-b)(a+b-1) )
- ( (a+b)(a-b-1) )
- ( (a-b)(a+b+1) )
- ( (a+b-1)^2 )
Medium · Level 71 · factorisation,common factor,monomials
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- (3ab(2a+3b))
- (3a(2ab+3b^2))
- (ab(6a+9b))
- (3ab(2a-3b))
What is the factorisation of (xy-2x+4y-8)?
Correct answer: A
Grouping gives (x(y-2)+4(y-2)). Exam tip: pair suitable terms correctly while grouping.
View question detailsWrite (36a^2-b^2) in factors.
Correct answer: A
Since (36a^2=(6a)^2), this is a difference of two squares. Exam tip: treat variable squares like ordinary squares.
View question detailsWhat is the correct factorised form of (k^2-15k+56)?
Correct answer: A
The numbers (-7) and (-8) have sum (-15) and product (56). Exam tip: when the constant term is positive, signs are the same.
View question detailsChoose the factorised form of (x^2-y^2+2y-1).
Correct answer: A
Treat (-y^2+2y-1) as (-(y-1)^2) to get (x^2-(y-1)^2). Exam tip: place the negative sign on the whole square.
View question detailsWhich is the correct factorisation of (2x^2+7x+3)?
Correct answer: A
Writing (2x^2+6x+x+3) and grouping gives the correct form. Exam tip: use the (ac) method to split the middle term.
View question detailsWhat are the factors of (3x^2+10x+8)?
Correct answer: A
Using (3x^2+6x+4x+8) gives common groups. Exam tip: you can also verify an option by expanding it.
View question detailsWhat is the complete factorised form of (12a^2-27b^2)?
Correct answer: A
Taking out (3) first gives (4a^2-9b^2). Exam tip: use both common factor and identity.
View question detailsChoose the factorised form of (a^2+b^2+2ab-c^2).
Correct answer: A
First convert (a^2+b^2+2ab) into ((a+b)^2). Exam tip: turn three terms into a perfect square before proceeding.
View question detailsWhich of the following trinomials can be factorised as a perfect square using the identity \,\(a^2+2ab+b^2=(a+b)^2\)?
Correct answer: A
In \(x^2+10x+25\), the first and last terms are \(x^2\) and \(5^2\), and the middle term is \(2\times x\times5=10x\). Hence it is \((x+5)^2\). Exam tip: compare the middle term with \(2ab\).
View question detailsWhat is the factorisation of (6pq+9p+4q+6)?
Correct answer: A
Grouping gives (3p(2q+3)+2(2q+3)). Exam tip: take out the common binomial once it appears.
View question detailsChoose the factorised form of (64m^3+125n^3).
Correct answer: A
It is ((4m)^3+(5n)^3). Exam tip: in the sum of cubes, the middle term of the second bracket is negative.
View question detailsWhich is the correct factorisation of (125x^3-216y^3)?
Correct answer: A
Here (125x^3=(5x)^3) and (216y^3=(6y)^3). Exam tip: in difference of cubes, signs in the second bracket are (+) and (+).
View question detailsWhat is the factorised form of (2a^2-11a+15)?
Correct answer: A
Using (2a^2-6a-5a+15) and grouping gives the answer. Exam tip: choose the pair with product (30) and sum (-11).
View question detailsWhich is the correct factorisation of (3y^2-14y-5)?
Correct answer: A
Expanding gives (3y^2-15y+y-5), which is (3y^2-14y-5). Exam tip: verify quickly by expanding the option.
View question detailsChoose the factorised form of (9x^2-1+6xy+y^2).
Correct answer: A
Write (9x^2+6xy+y^2) as ((3x+y)^2) and use difference of squares with (-1). Exam tip: arranging terms properly helps.
View question detailsWhat is the complete factorised form of (15x^2-20xy)?
Correct answer: A
Both terms have (5x) as the greatest common factor. Exam tip: take the common factor from both numerical and algebraic parts.
View question detailsWhat are the factors of (x^2+5x-24)?
Correct answer: A
The numbers (8) and (-3) have sum (5) and product (-24). Exam tip: with opposite signs, the larger magnitude gives the sign of the middle term.
View question detailsWhich is the correct factorisation of (a^2-b^2-a+b)?
Correct answer: A
Write (a^2-b^2) as ((a-b)(a+b)) and (-a+b) as (-(a-b)). Exam tip: take common ((a-b)) out.
View question detailsWhich is the correct factorised form of (6a^2b+9ab^2)?
Correct answer: A
The common factor is (3ab), leaving (2a+3b). In exams check both numerical and algebraic common factors.
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