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Algebraic Expressions and Identities Test - 17

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Algebraic Expressions and Identities Test - 17
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  • Question 1
    1 / -0
    (2x+3y)2=4x2+9y2+M(2x + 3y)^{2} = 4x^{2} + 9y^{2} + M, find M.
    Solution
    (2x+3y)2=4x2+9y2+12xy(2x + 3y)^{2} = 4x^{2} + 9y^{2} + 12xy,       ................. (a+b)2=a2+2ab+b2(a+b)^2= a^2+2ab+b^2

    hence, M=12xyM = 12xy
  • Question 2
    1 / -0
    Find the product of the following pairs of monomials.
    $$4p\  \&\  0$$
    Solution
    4p,04p, 0
    The product of the monomial pair is,
    =4×p×0=4\times p\times 0
    =0=0
  • Question 3
    1 / -0
    Find the product of the following pair of monomials.
    4p4p & 7p7p
    Solution
    Given: 4p,7p4p, 7p
    The product of the monomial pair is:
    =4×p×7×p=4\times p\times 7\times p
    =(4×7)×(p×p)=(4\times 7)\times(p\times p)
    =28p2=28p^2
  • Question 4
    1 / -0
    Find the product of the following pairs of monomials.
    4p,7pq4p, 7pq
    Solution
    4p,7pq4p, 7pq
    The product of the monomial pair is,
    =4×p×7×p×q=4\times p\times 7\times p\times q
    =(4×7)×(p×p×q)=(4\times 7)\times(p\times p\times q)
    =28p2q=28p^2q
  • Question 5
    1 / -0
    Multiply: $$4p, q + r$$
    Solution
    4p,q+r4p, q + r
    =4p×(q+r)=4p\times( q + r)
    =4pq+4pr=4pq+4pr
  • Question 6
    1 / -0
    The coefficient of x2x^2 in (23x2)(x25)(2-3x^2) (x^2-5) is :
    Solution
      (23x2)(x25)(2-3x^2)(x^2-5)
    =3x4+17x210=-3x^4+17x^2-10
    Coefficient is a constant number multiplied with a variable.
    Here as 1717 is multiplied with x2x^2. so it becomes the coefficient.
    Hence, DD is the correct answer.
  • Question 7
    1 / -0
    Find the product of the following pairs of monomials.
    4p3,3p4p^3, 3p
    Solution
    4p3,3p4p^3, 3p
    The product of the monomial pair is,
    =4×p×p×p×3×p=4\times p\times p\times p\times 3\times p
    =(4×3)×(p×p×p×p)=(4\times 3)\times(p\times p\times p\times p)
    =12p4=12p^4
  • Question 8
    1 / -0
    Obtain the product of: xy,yz,zxxy, yz, zx
    Solution
    xy,yz,zxxy, yz, zx
    =xy×yz×zx=xy\times yz\times zx
    =x2y2z2=x^2y^2z^2
  • Question 9
    1 / -0
    Find the product of the following pairs of monomials
    44 & 7p7p
    Solution
    4×7p=(4×7)p=28p\begin{aligned}{}4 \times 7p &= \left( {4 \times 7} \right)p\\ &= 28p\end{aligned}
  • Question 10
    1 / -0
    Obtain the product of: m,mn,mnpm, mn, mnp
    Solution
    m, mn,mnpm,  mn, mnp
    =m× mn×mnp=m\times  mn\times mnp
    =m3n2p=m^3n^2p
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