What is the factorised form of (s^2-12s+36)?
Correct answer: B
(36=6^2) and (-12s=-2\times6\times s). Exam tip: check the middle term in a perfect square.
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Factorisation
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Easy · Level 75 · minus perfect square,factorisation,identity
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- ((s+6)^2)
- ((s-6)^2)
- ((s-12)(s+3))
- ((s-3)(s-12))
Easy · Level 75 · factorisation,algebraic identities,quadratic trinomial,factor pairs,class 9 mathematics
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- 6 and 9
- 4 and 14
- 7 and 8
- 5 and 10
Easy · Level 75 · factorisation,common factor,greatest common factor,algebraic expressions,exponents
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- \(9a(3a^2-1)\)
- \(27a^2(a-1)\)
- \(9a^2(3a-a)\)
- \(9a^2(3a-1)\)
Easy · Level 75 · perfect square,two variables,factorisation
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- ((7u+v)^2)
- ((49u+v)^2)
- ((7u-v)^2)
- ((u+7v)^2)
Easy · Level 75 · signed trinomial,factorisation,quadratic
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- ((y+3)(y+8))
- ((y-3)(y-8))
- ((y-4)(y-6))
- ((y+2)(y+12))
Easy · Level 75 · factorisation,greatest common factor,algebraic expressions,monomials,class 9 mathematics
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- \(8mn(4m+5n)\)
- \(8mn(4m-5n)\)
- \(4mn(8m-5n)\)
- \(8mn(4m-10n)\)
Easy · Level 75 · perfect square,two variables,identity
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- ((x+4y)^2)
- ((x-2y)^2)
- ((x+2y)^2)
- ((x+2y)(x-2y))
Easy · Level 75 · algebraic identities, factorisation, difference of squares, class 9 mathematics, algebra
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- \(x^2-49\)
- \(x^2+49\)
- \(x^2+14x+49\)
- \(x^3-49\)
Easy · Level 75 · factorisation,algebraic identities,quadratic trinomials,class 9 mathematics,monic quadratic
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- \((t+3)(t-2)\)
- \((t-3)(t+2)\)
- \((t+1)(t-6)\)
- \((t+6)(t-1)\)
Easy · Level 75 · perfect square,minus square,factorisation
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- ((x+7)^2)
- ((x-7)^2)
- ((x-14)(x+49))
- ((x-49)^2)
Medium · Level 70 · factorisation,quadratic,algebraic identities
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- ( (x+2)(x+10) )
- ( (x+4)(x+5) )
- ( (x-4)(x-5) )
- ( (x+1)(x+20) )
Medium · Level 70 · difference of squares,factorisation,identity
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- ( (a-4)(a+4) )
- ( (a-8)(a+2) )
- ( (a+4)(a+4) )
- ( (a-2)(a+8) )
Medium · Level 70 · factorisation, algebraic identities, difference of squares, polynomials, class 9 mathematics
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- \(x^2-49\)
- \(x^2+49\)
- \(x^2-14x+49\)
- \(x^2+14x+49\)
Medium · Level 70 · quadratic,factorisation,middle term
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- ( (m+3)(m+8) )
- ( (m+4)(m+7) )
- ( (m-5)(m-6) )
- ( (m+5)(m+6) )
Medium · Level 70 · difference of squares,binomial,factorisation
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- ( (p-5q)(p+5q) )
- ( (p-25q)(p+q) )
- ( (p+5q)^2 )
- ( (p-5q)^2 )
Medium · Level 70 · quadratic,negative middle term,factorisation
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- ( (x-1)(x-10) )
- ( (x-2)(x-5) )
- ( (x+2)(x+5) )
- ( (x-3)(x-4) )
Medium · Level 70 · factorisation,difference of squares,algebraic identities,grade 9 mathematics
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- \((2r-9)(2r+9)\)
- \((2r-9)^2\)
- \((4r-9)(r+9)\)
- \((2r+9)^2\)
Medium · Level 70 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, binomial square
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- a² + 8a + 16
- a² + 8a + 15
- a² + 6a + 16
- a² − 8a + 15
Medium · Level 70 · common factor,monomial,factorisation
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- (3x(2x+5))
- (3(2x+5))
- (x(6x+15))
- (5x(2x+3))
Medium · Level 70 · grouping,factorisation,common binomial
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- ( (a+d)(b+c) )
- ( (a+b)(c+d) )
- ( (a+c)(b+d) )
- ( (a-d)(b-c) )
Which pair is correct for factorising \(x^2+15x+56\)?
Correct answer: C
To factorise \(x^2+15x+56\) as \((x+a)(x+b)\), we need \(a+b=15\) and \(ab=56\). Since \(7+8=15\) and \(7\times8=56\), \(x^2+15x+56=(x+7)(x+8)\). In option A, 6 and 9 add to 15, but their product is 54, not 56. Exam tip: for such trinomials, check that the sum matches the middle coefficient and the product matches the constant term.
View question detailsWhat is obtained by taking out the common factor from (27a^3-9a^2)?
Correct answer: D
The greatest common factor of \(27a^3\) and \(-9a^2\) is \(9a^2\). Hence, \(27a^3-9a^2=9a^2(3a-1)\). In option A, \(9a\) is a common factor but not the greatest one, so the remaining bracket should be different. Exam tip: use the HCF of the numerical coefficients and the lowest power of each common variable.
View question detailsWhose perfect square is (49u^2+14uv+v^2)?
Correct answer: A
(49u^2=(7u)^2), (v^2), and (14uv=2\times7u\times v). Exam tip: take square roots of both square terms.
View question detailsWhat are the correct factors of (y^2-11y+24)?
Correct answer: B
(-3-8=-11) and ((-3)\times(-8)=24). Exam tip: two negative signs give a positive last term.
View question detailsWhat is the simple factorised form of (32m^2n-40mn^2)?
Correct answer: B
The greatest common factor of \(32m^2n\) and \(-40mn^2\) is \(8mn\). On factoring out \(8mn\), we get \(32m^2n\div 8mn=4m\) and \(-40mn^2\div 8mn=-5n\). Hence, \(32m^2n-40mn^2=8mn(4m-5n)\). In option A, the positive sign would give \(+40mn^2\) as the second term. Exam tip: expand the factors to check whether they reproduce the original expression.
View question detailsIn which form will (x^2+4xy+4y^2) be written?
Correct answer: C
(4y^2=(2y)^2) and (4xy=2\times x\times2y). Exam tip: take the square root of the second square term correctly.
View question detailsWhich of the following expressions can be factorised using the identity \(p^2-q^2=(p+q)(p-q)\)?
Correct answer: A
\(x^2-49=x^2-7^2\), so it is a difference of two squares and becomes \((x+7)(x-7)\). \(x^2+49\) is a sum of squares. In exams, first check whether the constant is a perfect square.
View question detailsWhat are the factors of \(t^2+t-6\)?
Correct answer: A
To factorise \(t^2+t-6\), find two numbers whose product is \(-6\) and whose sum is \(1\). They are \(3\) and \(-2\). Hence, \(t^2+t-6=(t+3)(t-2)\). In option B, \(-3+2=-1\), so it produces \(t^2-t-6\). Exam tip: expand the factors once to check the middle term and the constant term.
View question detailsWhat is the correct factorised form of (x^2-14x+49)?
Correct answer: B
(49=7^2) and (-14x=-2\times7\times x). Exam tip: identify ((a-b)^2) from the negative middle term.
View question detailsWhat is the correct factorised form of (x^2+9x+20)?
Correct answer: B
The numbers (4) and (5) have sum (9) and product (20). Exam tip: check both sum and product while splitting the middle term.
View question detailsWrite (a^2-16) in factors.
Correct answer: A
It is (a^2-4^2) so the difference of squares identity applies. Exam tip: remember (p^2-q^2=(p-q)(p+q)).
View question detailsWhich of the following expressions is a difference of two squares and can therefore be factorised into the product of two binomials?
Correct answer: A
\(x^2-49=x^2-7^2\), so it fits \(a^2-b^2=(a-b)(a+b)\). \(x^2+49\) is a sum of squares, not this identity. Exam tip: check for two perfect squares separated by a minus sign.
View question detailsWhat are the factors of (m^2+11m+30)?
Correct answer: D
The numbers (5) and (6) have sum (11) and product (30). Exam tip: for a positive middle term choose signs carefully.
View question detailsChoose the factorised form of (p^2-25q^2).
Correct answer: A
Writing (25q^2) as ((5q)^2) gives the difference of squares identity. Exam tip: first see both terms as squares.
View question detailsWhich is the correct factorisation of (x^2-7x+10)?
Correct answer: B
The numbers (-2) and (-5) have sum (-7) and product (10). Exam tip: a negative middle term may need both negative signs.
View question detailsWrite (4r^2-81) in factors.
Correct answer: A
This is a difference of two perfect squares because \(4r^2=(2r)^2\) and \(81=9^2\). Applying \(a^2-b^2=(a-b)(a+b)\) with \(a=2r\) and \(b=9\) gives \(4r^2-81=(2r-9)(2r+9)\). The close distractor \((2r-9)^2\) expands to \(4r^2-36r+81\), which has a middle term and a positive constant term. Exam tip: before factorising, check whether both terms are perfect squares separated by a minus sign.
View question detailsWhich of the following trinomials can be identified as the perfect square of a binomial?
Correct answer: A
In a² + 8a + 16, the first and last terms are a² and 4². The middle term is 2 × a × 4 = 8a, so it equals (a + 4)². In exams, also check the sign of the middle term.
View question detailsChoose the correct form of (6x^2+15x) after taking out the common factor.
Correct answer: A
Both terms have (3x) as the common factor. Exam tip: first take out the greatest common factor.
View question detailsWhat is the factorisation of (ab+ac+db+dc) by grouping?
Correct answer: A
Taking (a) from the first two terms and (d) from the last two gives common (b+c). Exam tip: aim to create a common binomial.
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