Which answer is correct after factorising (2x^2+9x+10)?
Correct answer: A
Expanding gives (2x^2+4x+5x+10=2x^2+9x+10). Exam tip: verify the answer by multiplication.
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Factorisation
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Expert · Level 71 · quadratic factorisation,verification,middle term
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- ((2x+5)(x+2))
- ((2x+2)(x+5))
- ((x+5)(x+4))
- ((2x+10)(x+1))
Expert · Level 71 · algebraic identities, factorisation, difference of squares, class 9 mathematics, conceptual question
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- Sum of two perfect-square terms
- Difference of two perfect-square terms
- Three terms whose middle term is twice the product of two terms
- Difference of two cube terms
Expert · Level 71 · grouping,difference of squares,factorisation
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- ((x+y)(x-y+2))
- ((x-y)(x+y+2))
- ((x+y+2)(x-y))
- ((x+y)(x-y-2))
Expert · Level 71 · factorisation by grouping,common binomial,algebra
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- ((m+q)(n+p))
- ((m+n)(p+q))
- ((m+p)(n+q))
- ((mn+q)(p+1))
Expert · Level 71 · factorisation,sum of cubes,algebraic identities,perfect cubes,class 9 mathematics
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- \((2x+3y)(4x^2-6xy+9y^2)\)
- \((2x-3y)(4x^2+6xy+9y^2)\)
- \((2x+3y)(4x^2+6xy+9y^2)\)
- \((8x+27y)(x^2-xy+y^2)\)
Expert · Level 71 · difference of cubes,cubic factorisation,identity
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- ((4a-5b)(16a^2+20ab+25b^2))
- ((4a+5b)(16a^2-20ab+25b^2))
- ((8a-25b)(8a^2+ab+b^2))
- ((4a-5b)^3)
Expert · Level 71 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, binomial square
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- \(x^2 + 10x + 25\)
- \(x^2 + 10x + 15\)
- \(x^2 + 5x + 25\)
- \(x^2 + 10x - 25\)
Expert · Level 71 · common factor,monomial factorisation,algebra
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- (7x(x-4y))
- (7(x^2-4y))
- (x(7x-28))
- (7xy(x-4))
Expert · Level 71 · combined identity,perfect square,difference of squares
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- ((x+2y-3z)(x+2y+3z))
- ((x-2y-3z)(x-2y+3z))
- ((x+2y)^2-3z)
- ((x+3z)(2y-3z))
Expert · Level 71 · grouping,difference of squares,factorisation
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- ((a-b)(a+b-1))
- ((a+b)(a-b-1))
- ((a-b)(a+b+1))
- ((a-1)(a+b))
Expert · Level 71 · factorisation, algebraic identities, perfect square trinomial, class 9 mathematics, polynomial classification
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- \(9a^2-24ab+16b^2\)
- \(9a^2-24ab+12b^2\)
- \(9a^2+24ab+16b^2\)
- \(9a^2-12ab+16b^2\)
Expert · Level 71 · quadratic factorisation,negative constant,expert
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- ((3x-5)(6x+2))
- ((6x-5)(3x+2))
- ((9x+2)(2x-5))
- ((18x+5)(x-2))
Expert · Level 71 · algebraic identities,factorisation,perfect square trinomial,class 9 mathematics,polynomial identities
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- \(a^2+14a+49\)
- \(a^2+14a+14\)
- \(a^2+7a+49\)
- \(a^2+14a-49\)
Expert · Level 71 · perfect cube,cube identity,factorisation
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- ((2a+b)^3)
- ((2a-b)^3)
- ((8a+b)^3)
- ((a+2b)^3)
Expert · Level 71 · factorisation, algebraic identities, difference of squares, conjugate binomials, class 9 mathematics
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- \(49a^2-16b^2\)
- \(25x^2+4y^2\)
- \(9p^2+6pq+q^2\)
- \(r^2+2rs-s^2\)
Expert · Level 71 · perfect square,difference of squares,factorisation
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- ((2x+y-4)(2x+y+4))
- ((2x-y-4)(2x-y+4))
- ((4x+y-16)(x+y+1))
- ((2x+y)^2-4)
Expert · Level 71 · factorisation, algebraic identities, quadratic trinomials, integer coefficients, class 9 mathematics
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- \(x^2-9y^2\)
- \(x^2+5x+6\)
- \(x^2+xy+y^2\)
- \(x^2-7x+12\)
Expert · Level 71 · factorisation, algebraic identities, difference of squares, class 9 mathematics, polynomials
View options
- \(4p^2-25q^2\)
- \(4p^2+25q^2\)
- \(4p^2+20pq+25q^2\)
- \(4p^2-20pq+25q^2\)
Expert · Level 71 · quadratic factorisation,two variables,opposite signs
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- ((5m+2n)(m-3n))
- ((5m-2n)(m+3n))
- ((m-6n)(5m+n))
- ((5m-6n)(m+n))
Expert · Level 71 · combined identity,perfect square,difference of squares
View options
- ((x+3-y)(x+3+y))
- ((x-3-y)(x-3+y))
- ((x+3)^2-y)
- ((x+y+3)(x-y-3))
Which type of expression can be factorised directly using the identity \(a^2-b^2=(a-b)(a+b)\)?
Correct answer: B
In \(a^2-b^2\), both terms are perfect squares joined by subtraction, so it becomes \((a-b)(a+b)\). A sum of squares does not use this identity. Exam tip: check the sign between the squared terms first.
View question detailsWhat will be the factorised form of (x^2-y^2+2x+2y)?
Correct answer: A
Write it as ((x+y)(x-y)+2(x+y)), then take ((x+y)) common. Exam tip: identify the difference of squares first.
View question detailsWrite (mn+mp+qn+qp) in factors.
Correct answer: A
Grouping gives (m(n+p)+q(n+p)), so the factor is ((m+q)(n+p)). Exam tip: look for the common binomial bracket.
View question detailsWhich is the factorised form of (8x^3+27y^3)?
Correct answer: A
The expression is \(8x^3+27y^3=(2x)^3+(3y)^3\). Applying the sum-of-cubes identity \(a^3+b^3=(a+b)(a^2-ab+b^2)\) gives \((2x+3y)(4x^2-6xy+9y^2)\). Hence, option A is correct. Option B is associated with the difference-of-cubes identity \(a^3-b^3\), so it does not apply here. Exam tip: in a sum of cubes, the middle term of the second factor is negative.
View question detailsChoose the correct factorised form of (64a^3-125b^3).
Correct answer: A
Here (64a^3=(4a)^3) and (125b^3=(5b)^3). Exam tip: in the difference formula, the second bracket has positive (20ab).
View question detailsWhich of the following trinomials is a perfect-square trinomial that can be factorised as the square of a binomial?
Correct answer: A
A perfect-square trinomial has the form \(x^2+2ax+a^2\). Here, \(10x=2\times5\times x\) and \(25=5^2\), so \(x^2+10x+25=(x+5)^2\). In option B, the middle term is \(10x\), but the constant term should be \(25\), not \(15\). Exam tip: square half of the middle-term coefficient and compare it with the constant term.
View question detailsWhat is the factorised form of (7x^2-28xy)?
Correct answer: A
Both terms have common factor (7x). Exam tip: take out both numerical and variable factors.
View question detailsChoose the factorised form of (x^2+4xy+4y^2-9z^2).
Correct answer: A
First (x^2+4xy+4y^2=(x+2y)^2), and (9z^2=(3z)^2). Exam tip: apply two identities in order.
View question detailsWhat will be the factorised form of (a^2-b^2-a+b)?
Correct answer: A
Write it as ((a-b)(a+b)-(a-b)), then take ((a-b)) common. Exam tip: also convert the last two terms into a group.
View question detailsWhich of the following trinomials is correctly identified as a perfect-square trinomial?
Correct answer: A
Here \(9a^2=(3a)^2\) and \(16b^2=(4b)^2\). The middle term is \(-2(3a)(4b)=-24ab\), so it matches \((3a-4b)^2\). In exams, always check the sign of the middle term.
View question detailsFactorise (18x^2-21x-10).
Correct answer: B
((6x-5)(3x+2)) gives (18x^2+12x-15x-10). Exam tip: confirm that the middle term becomes (-21x).
View question detailsWhich of the following trinomials can be factorised as the square of a single binomial?
Correct answer: A
In \(a^2+14a+49\), \(49=7^2\) and the middle term is \(14a=2\times a\times7\). Hence it equals \((a+7)^2\). In B, the constant term is not \(7^2\). Exam tip: check the \(2ab\) term.
View question detailsWhat is the factorised form of (8a^3+12a^2b+6ab^2+b^3)?
Correct answer: A
It is ((2a)^3+3(2a)^2b+3(2a)b^2+b^3). Exam tip: identify cube coefficients (1), (3), (3), (1).
View question detailsWhich of the following expressions is in the form of a difference of two squares and can be factorised into a product of conjugate binomials?
Correct answer: A
\(49a^2-16b^2=(7a)^2-(4b)^2\). Using \(A^2-B^2=(A-B)(A+B)\), it becomes \((7a-4b)(7a+4b)\). Option C is a perfect square, not a difference. Exam tip: first identify whether both terms are squares.
View question detailsWhich is the factorised form of (4x^2+4xy+y^2-16)?
Correct answer: A
First (4x^2+4xy+y^2=(2x+y)^2), and (16=4^2). Exam tip: apply difference of squares at the end.
View question detailsWhich of the following expressions cannot be factorised as a product of two binomials when both binomials have integer coefficients?
Correct answer: C
For \(x^2+xy+y^2\), integer values \(a,b\) would need \(a+b=1\) and \(ab=1\), but no integer pair satisfies both. Option A uses difference of squares. Exam tip: check the required sum and product of coefficients.
View question detailsWhich of the following expressions is in the form of a difference of squares, \(a^2-b^2\), and can therefore be factorised using the identity \((a-b)(a+b)\)?
Correct answer: A
\(4p^2-25q^2=(2p)^2-(5q)^2\), so it is a difference of squares and factorises as \((2p-5q)(2p+5q)\). Options C and D are perfect-square trinomials. Exam tip: identify square terms first, then check for a minus sign between them.
View question detailsWhich is the correct factorised form of (5m^2-13mn-6n^2)?
Correct answer: A
((5m+2n)(m-3n)) gives (5m^2-15mn+2mn-6n^2). Exam tip: use opposite signs for a negative constant term.
View question detailsWhat is the factorised form of (x^2+6x+9-y^2)?
Correct answer: A
Here (x^2+6x+9=(x+3)^2), then difference of squares applies. Exam tip: first convert the trinomial into a perfect square.
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