The sum of two algebraic expressions is x2- 4. If one of them is x2+ 4, then find the other expression.
Answers
Answer:
-8
Step-by-step explanation:
Let the another number be a
x²+4+a= x²-4
Transpose -4 to LHS and x² and a to RHS
4+4= x²-x²-a
8= -a
Transpose both the sides
a= -8
Answer:
ANSWER:
(i) y − z
(ii)
(iii) z2
(iv)
(v) x2 + y2
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)
Page No 234:
Question 2:
(i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
(a) x − 3 (b) 1 + x + x2 (c) y − y3
(d) (e) − ab + 2b2 − 3a2
(ii) Identify terms and factors in the expressions given below:
(a) − 4x + 5 (b) − 4x + 5y (c) 5y + 3y2
(d) (e) pq + q
(f) 1.2 ab − 2.4 b + 3.6 a (g)
(h) 0.1p2 + 0.2 q2
ANSWER:
(i)
(a)
(b)
(c)
(d)
(e)
(ii)
Row
Expression
Terms
Factors
(a)
− 4x + 5
− 4x
5
− 4, x
5
(b)
− 4x + 5y
− 4x
5y
− 4, x
5, y
(c)
5y + 3y2
5y
3y2
5, y
3, y, y
(d)
xy + 2x2y2
xy
2x2y2
x, y
2, x, x, y, y
(e)
pq + q
pq
q
p, q
q
(f)
1.2ab − 2.4b + 3.6a
1.2ab
− 2.4b
3.6a
1.2, a, b
− 2.4, b
3.6, a
(g)
(h)
0.1p2 + 0.2q2
0.1p2
0.2q2
0.1, p, p
0.2, q, q
Page No 235:
Question 3:
Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 − 3t2 (ii) 1 + t + t2 + t3 (iii) x + 2xy+ 3y
(iv) 100m + 1000n (v) − p2q2 + 7pq (vi) 1.2a + 0.8b
(vii) 3.14 r2 (viii) 2 (l + b) (ix) 0.1y + 0.01 y2
ANSWER:
Row
Expression
Terms
Coefficients
(i)
5 − 3t2
− 3t2
− 3
(ii)
1 + t + t2 + t3
t
t2
t3
1
1
1
(iii)
x + 2xy + 3y
x
2xy
3y
1
2
3
(iv)
100m + 1000n
100m
1000n
100
1000
(v)
− p2q2 + 7pq
− p2q2
7pq
− 1
7
(vi)
1.2a +0.8b
1.2a
0.8b
1.2
0.8
(vii)
3.14 r2
3.14 r2
3.14
(viii)
2(l + b)
2l
2b
2
2
(ix)
0.1y + 0.01y2
0.1y
0.01y2
0.1
0.01
Page No 235:
Question 4:
(a) Identify terms which contain x and give the coefficient of x.
(i) y2x + y (ii) 13y2− 8yx (iii) x + y + 2
(iv) 5 + z + zx (v) 1 + x+ xy (vi) 12xy2 + 25
(vii) 7x + xy2
(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8 − xy2 (ii) 5y2 + 7x (iii) 2x2y −15xy2 + 7y2
ANSWER:
(a)
Row
Expression
Terms with x
Coefficient of x
(i)
y2x + y
y2x
y2
(ii)
13y2 − 8yx
− 8yx
−8y
(iii)
x + y + 2
x
1
(iv)
5 + z + zx
zx
z
(v)
1 + x + xy
x
xy
1
y
(vi)
12xy2 + 25
12xy2
12y2
(vii)
7x+ xy2
7x
xy2
7
y2
(b)
Row
Expression
Terms with y2
Coefficient of y2
(i)
8 − xy2
−xy2
− x
(ii)
5y2 + 7x
5y2
5
(iii)
2x2y + 7y2
−15xy2
7y2
−15xy2
7
−15x
Page No 235:
Question 5:
Classify into monomials, binomials and trinomials.
(i) 4y − 7z (ii) y2 (iii) x + y − xy
(iv) 100 (v) ab − a − b (vi) 5 − 3t
(vii) 4p2q − 4pq2 (viii) 7mn (ix) z2 − 3z + 8
(x) a2 + b2 (xi) z2 + z (xii) 1 + x + x2
ANSWER:
The monomials, binomials, and trinomials have 1, 2, and 3 unlike terms in it respectively.
(i) 4y − 7z
Binomial
(ii) y2
Monomial
(iii) x + y − xy
Trinomial
(iv) 100
Monomial
(v) ab − a − b
Trinomial
(vi) 5 − 3t
Binomial
(vii) 4p2q − 4pq2
Binomial
(viii) 7mn
Monomial
(ix) z2 − 3z + 8
Trinomial
(x) a2 + b2
Binomial
(xi) z2 + z
Binomial
(xii) 1 + x + x2
Trinomial
Page No 235:
Question 6:
State whether a given pair of terms is of like or unlike terms.
(i) 1, 100 (ii) (iii) − 29x, − 29y
(iv) 14xy, 42yx (v) 4m2p, 4mp2 (vi) 12xz, 12 x2z2
ANSWER:
The terms which have the same algebraic factors are called like terms. However, when the terms have different algebraic factors, these are called unlike terms.
(i) 1, 100
Like
(ii) − 7x,
Like
(iii) −29x, −29y
Unlike
(iv) 14xy, 42yx
Like
(v) 4m2p, 4mp2
Unlike
(vi) 12xz, 12x2z2
Unlike
Page No 235:
Question 7:
Identify like terms in the following:
(a) −xy2, − 4yx2, 8x2, 2xy2, 7y, − 11x2, − 100x, −11yx, 20x2y, −6x2, y, 2xy,3x
(b) 10pq, 7p, 8q, − p2q2, − 7qp, − 100q, − 23, 12q2p2, − 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
ANSWER:
(a) −xy2, 2xy2
−4yx2, 20x2y
8x2, −11x2, −6x2
7y, y
−100x, 3x
−11xy, 2xy
(b) 10pq, −7qp, 78qp
7p, 2405p
8q, −100q
−p2q2, 12p2q2
−23, 41
−5p2, 701p2
13p2q, qp2
-
-
-
-
-
-
(iv)
7n + 20
27
34
41
48
-
-
-
-
-
-
(v)
n2 + 1
2
5
10
17
-
-
-
-
10, 001
-