What are the factors of (x^2-49y^2)?
Correct answer: A
Since (49y^2=(7y)^2), the difference of squares identity applies. Exam tip: spot forms like (x^2-a^2) quickly.
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Factorisation
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Medium · Level 70 · difference of squares,factorisation,binomial
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- ( (x-7y)(x+7y) )
- ( (x-49y)(x+y) )
- ( (x+7y)(x+7y) )
- ( (x-7y)(x-7y) )
Medium · Level 70 · quadratic,middle term,signs
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- ( (n-7)(n+4) )
- ( (n+7)(n-4) )
- ( (n-14)(n+2) )
- ( (n-1)(n-28) )
Medium · Level 70 · perfect square trinomial,identity,factorisation
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- ( (3a+4)^2 )
- ( (3a-4)^2 )
- ( (9a+4)(a+4) )
- ( (3a+8)(3a+2) )
Medium · Level 70 · grouping,factorisation,common binomial
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- ( (2x+5)(y+3) )
- ( (2x+3)(y+5) )
- ( (x+5)(2y+3) )
- ( (2x-5)(y-3) )
Medium · Level 70 · perfect square,negative middle term,factorisation
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- ( (4u+3v)^2 )
- ( (4u-3v)^2 )
- ( (16u-9v)^2 )
- ( (4u-9v)(4u+v) )
Medium · Level 70 · quadratic,factorisation,sign choice
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- ( (s+7)(s-5) )
- ( (s-7)(s+5) )
- ( (s-1)(s-35) )
- ( (s+35)(s-1) )
Medium · Level 70 · algebraic identities, factorisation, perfect square trinomial, class 9 mathematics, difference of squares
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- \(m^2-2mn+n^2\)
- \(m^2+2mn-n^2\)
- \(m^2-n^2\)
- \(m^2+mn+n^2\)
Medium · Level 70 · factorisation, algebraic identities, difference of cubes, class 9 mathematics, perfect cubes
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- \(x^3+8\)
- \(27a^3-8b^3\)
- \(m^2-16\)
- \(p^3+q^3\)
Medium · Level 70 · factorisation,algebraic identities,difference of squares,perfect square,class 9 mathematics
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- \((x+y-5)(x+y+5)\)
- \((x-y-5)(x-y+5)\)
- \((x+y-25)(x+y+1)\)
- \((x+y)^2+25\)
Medium · Level 70 · perfect square,difference of squares,factorisation
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- ( (2x+3-y)(2x+3+y) )
- ( (2x-3-y)(2x-3+y) )
- ( (4x+9-y)(x+1+y) )
- ( (2x+y+3)^2 )
Medium · Level 70 · common factor,monomial,factorisation
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- (3a(a+4b))
- (3(a^2+4ab))
- (a(3a+12b))
- (6a(a+2b))
Medium · Level 70 · quadratic,factorisation,signs
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- ( (x-6)(x-7) )
- ( (x+6)(x+7) )
- ( (x-3)(x-14) )
- ( (x-2)(x-21) )
Medium · Level 70 · grouping,common binomial,factorisation
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- ( (5m+3)(n-2) )
- ( (5m-3)(n+2) )
- ( (m+3)(5n-2) )
- ( (5m+6)(n-1) )
Medium · Level 70 · factorisation, algebraic identities, perfect square trinomial, error analysis, class 9 mathematics
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- यह पूर्ण वर्ग त्रिपद है; सही गुणनखंडन \((7p-5q)^2\) है।
- यह वर्गों का अंतर है; दिया गया गुणनखंडन सही है।
- मध्य पद धनात्मक होना चाहिए, इसलिए सही गुणनखंडन \((7p+5q)^2\) है।
- स्थिर पद \(25q^2\) का गुणनखंडन नहीं किया जा सकता।
Medium · Level 70 · quadratic,factorisation,middle term
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- ( (q+8)(q-7) )
- ( (q-8)(q+7) )
- ( (q+4)(q-14) )
- ( (q-1)(q+56) )
Medium · Level 70 · sum of cubes,identity,factorisation
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- ( (a+4)(a^2-4a+16) )
- ( (a-4)(a^2+4a+16) )
- ( (a+4)(a^2+4a+16) )
- ( (a+8)(a^2-8a+64) )
Medium · Level 70 · difference of cubes,identity,factorisation
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- ( (b-3)(b^2+3b+9) )
- ( (b+3)(b^2-3b+9) )
- ( (b-9)(b^2+9b+81) )
- ( (b-3)(b^2-3b+9) )
Medium · Level 70 · quadratic,factorisation,middle term
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- ( (x+2)(x+4) )
- ( (x-2)(x-4) )
- ( (x+1)(x+8) )
- ( (x+3)(x+3) )
Medium · Level 70 · common factor,polynomial,factorisation
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- (7xy(x-3y+2))
- (7x(xy-3y^2+2y))
- (xy(7x-21y+14))
- (14xy(x-y+1))
Medium · Level 70 · difference of squares,factorisation,identity
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- ( (t-8)(t+8) )
- ( (t-32)(t+2) )
- ( (t+8)^2 )
- ( (t-8)^2 )
What is the correct factorised form of (n^2-3n-28)?
Correct answer: A
The numbers (-7) and (4) have sum (-3) and product (-28). Exam tip: negative product means opposite signs.
View question detailsChoose the factorised form of (9a^2+24a+16).
Correct answer: A
It is ((3a)^2+2\cdot3a\cdot4+4^2). Exam tip: when first and last terms are squares, check the middle term.
View question detailsWhat is the factorisation of (2xy+6x+5y+15)?
Correct answer: A
Grouping gives (2x(y+3)+5(y+3)). Exam tip: group terms until a common bracket appears.
View question detailsWhich is the correct factorisation of (16u^2-24uv+9v^2)?
Correct answer: B
It is ((4u)^2-2\cdot4u\cdot3v+(3v)^2). Exam tip: for a negative middle term, check ((a-b)^2).
View question detailsWrite (s^2-2s-35) in factors.
Correct answer: B
The numbers (-7) and (5) have sum (-2) and product (-35). Exam tip: the sign of the larger magnitude decides the middle term sign.
View question detailsWhich of the following expressions can be factorised as \((m-n)^2\)?
Correct answer: A
The identity is \((m-n)^2=m^2-2mn+n^2\), so option A is a perfect-square trinomial. Option C factorises as \((m-n)(m+n)\), making it a difference of squares, not a square. Exam tip: check that the middle term is \(-2mn\).
View question detailsWhich of the following expressions can be factorised using the identity for the difference of cubes?
Correct answer: B
Since \(27a^3=(3a)^3\) and \(8b^3=(2b)^3\), the expression has the form \(A^3-B^3\). Thus it factors as \((3a-2b)(9a^2+6ab+4b^2)\). Exam tip: first identify perfect cubes; \(m^2-16\) is a difference of squares, not cubes.
View question detailsWhich is the correct factorised form of (x^2+2xy+y^2-25)?
Correct answer: A
In \(x^2+2xy+y^2-25\), the first three terms form \((x+y)^2\), and \(25=5^2\). Hence the expression is \((x+y)^2-5^2\). Using \(a^2-b^2=(a-b)(a+b)\), we get \((x+y-5)(x+y+5)\). Option B would involve \((x-y)^2\), whose middle term is \(-2xy\), so it is incorrect. Exam tip: first recognise expressions of the form \(x^2\pm2xy+y^2\) as perfect squares.
View question detailsWhat will be the factors of (4x^2+12x+9-y^2)?
Correct answer: A
Write (4x^2+12x+9) as ((2x+3)^2) and then use difference of squares. Exam tip: forming a perfect square first is useful.
View question detailsWhat is the form of (3a^2+12ab) after taking the common factor?
Correct answer: A
The greatest common factor of both terms is (3a). Exam tip: avoid taking an incomplete common factor.
View question detailsWhich is the correct factorisation of (x^2-13x+42)?
Correct answer: A
The numbers (-6) and (-7) have sum (-13) and product (42). Exam tip: if the constant is positive and the middle term is negative, both signs may be negative.
View question detailsWhat is the factorised form of (5mn-10m+3n-6)?
Correct answer: A
Grouping gives (5m(n-2)+3(n-2)). Exam tip: arrange terms so that a common bracket appears.
View question detailsA student claims that \(49p^2-70pq+25q^2=(7p-5q)(7p+5q)\). What is the error in the factorisation?
Correct answer: A
Using \((a-b)^2=a^2-2ab+b^2\), with \(a=7p\) and \(b=5q\), gives \(49p^2-70pq+25q^2\). But \((7p-5q)(7p+5q)=49p^2-25q^2\), so it has no middle term. Exam tip: check whether the middle term equals \(-2ab\).
View question detailsConvert (q^2+q-56) into factors.
Correct answer: A
The numbers (8) and (-7) have sum (1) and product (-56). Exam tip: even when the coefficient of (q) is (1), do not skip middle-term checking.
View question detailsWhat is the factorised form of (a^3+64)?
Correct answer: A
Since (64=4^3), this is a sum of cubes. Exam tip: keep the signs (-) then (+) in the second bracket.
View question detailsWhich is the correct factorisation of (b^3-27)?
Correct answer: A
Here (27=3^3) and it is a difference of cubes. Exam tip: in (a^3-b^3), the second bracket is (a^2+ab+b^2).
View question detailsChoose the factorised form of (x^2+6x+8).
Correct answer: A
The numbers (2) and (4) have sum (6) and product (8). Exam tip: check all options even in simple products.
View question detailsWhat is the best factorised form of (7x^2y-21xy^2+14xy)?
Correct answer: A
All three terms have (7xy) as the greatest common factor. Exam tip: the best factorised form takes out the greatest common factor.
View question detailsWhich is the correct factorisation of (t^2-64)?
Correct answer: A
Since (64=8^2), the difference of squares identity applies. Exam tip: recognising square numbers quickly saves time.
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