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Identify the terms, their coefficients for each of the following expressions.
(i) 5xyz2 − 3zy
(ii) 1 + x + x2
(iii) 4x2y2 − 4x2y2z2+ z2
(iv) 3 − pq + qr − rp
(v) 
(vi) 0.3a − 0.6ab + 0.5b
The terms and the respective coefficients of the given expressions are as follows.
|
- |
Terms |
Coefficients |
|
(i) |
5xyz2 − 3zy |
5 − 3 |
|
(ii) |
1 x x2 |
1 1 1 |
|
(iii) |
4x2y2 − 4x2y2z2 z2 |
4 − 4 1 |
|
(iv) |
3 − pq qr − rp |
3 −1 1 −1 |
|
(v) |
− xy |
− 1 |
|
(vi) |
0.3a − 0.6ab 0.5b |
0.3 − 0.6 0.5 |
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y − 3y2, 2y − 3y2 + 4y3, 5x − 4y + 3xy, 4z − 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q
The given expressions are classified as
Monomials: 1000, pqr
Binomials: x + y, 2y − 3y2, 4z − 15z2, p2q + pq2, 2p + 2q
Trinomials: 7 + y + 5x, 2y − 3y2 + 4y3, 5x − 4y + 3xy
Polynomials that do not fit in any of these categories are
x + x2 + x3 + x4, ab + bc + cd + da
Add the following.
(i) ab − bc, bc − ca, ca − ab
(ii) a − b + ab, b − c + bc, c − a + ac
(iii) 2p2q2 − 3pq + 4, 5 + 7pq − 3p2q2
(iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
The given expressions written in separate rows, with like terms one below the other and then the addition of these expressions are as follows.
(i)
Thus, the sum of the given expressions is 0.
(ii)
Thus, the sum of the given expressions is ab + bc + ac.
(iii)
Thus, the sum of the given expressions is −p2q2 + 4pq + 9.
(iv)
Thus, the sum of the given expressions is 2(l2 + m2 + n2 + lm + mn + nl).
(a) Subtract 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3
(b) Subtract 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz
(c) Subtract 4p2q − 3pq + 5pq2 − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq2 + 5p2q
The given expressions in separate rows, with like terms one below the other and then the subtraction of these expressions is as follows.
(a)
(b)
(c)
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