Algebraic Expressions - Class 7 Mathematics - Chapter 10 - Notes, NCERT Solutions & Extra Questions
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Examples - Algebraic Expressions | NCERT | Mathematics | Class 7
Identify, in the following expressions, terms which are not constants. Give their numerical coefficients:
$x y+4,13-y^{2}, 13-y+5 y^{2}, 4 p^{2} q-3 p q^{2}+5$
To identify the terms that are not constants and provide their numerical coefficients, we will analyze each expression separately:
Expression: $x y+4$
Not a constant term: $xy$
Numerical coefficient: 1.
Expression: $13-y^2$
Not a constant term: $-y^2$
Numerical coefficient: -1.
Expression: $13-y+5y^2$
Not a constant term: $-y$, $5y^2$
Numerical coefficients: -1 for $-y$, and 5 for $5y^2$.
Expression: $4p^2q - 3pq^2 + 5$
Not a constant terms: $4p^2q$, $-3pq^2$
Numerical coefficients: 4 for $4p^2q$, and -3 for $-3pq^2$.
In summary:
For $xy+4$, the non-constant term is $xy$ with a coefficient of 1.
For $13-y^2$, the non-constant term is $-y^2$ with a coefficient of -1.
For $13-y+5y^2$, the non-constant terms are $-y$ with a coefficient of -1, and $5y^2$ with a coefficient of 5.
For $4p^2q - 3pq^2 + 5$, the non-constant terms are $4p^2q$ with a coefficient of 4, and $-3pq^2$ with a coefficient of -3.
What are the coefficients of $x$ in the following expressions?
(a) $4 x-3 y, 8-x+y, y^{2} x-y, 2 z-5 x z$
(b) What are the coefficients of $y$ in the following expressions?
$4 x-3 y, 8+y z, y z^{2}+5, m y+m$
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State with reasons, which of the following pairs of terms are of like terms and which are of unlike terms:
(i) $7 x, 12 y$
(ii) $15 x,-21 x$
(iii) $-4 a b, 7 b a$
(iv) $3 x y, 3 x$
(v) $6 x y^{2}, 9 x^{2} y$
(vi) $p q^{2},-4 p q^{2}$
(vii) $m n^{2}, 10 m n$
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Find the values of the following expressions for $x=2$.
(i) $x+4$
(ii) $4 x-3$
(iii) $19-5 x^{2}$
(iv) $100-10 x^{3}$
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Find the value of the following expressions when $n=-2$.
(i) $5 n-2$
(ii) $5 n^{2}+5 n-2$
(iii) $n^{3}+5 n^{2}+5 n-2$
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Find the value of the following expressions for $a=3, b=2$.
(i) $a+b$
(ii) $7 a-4 b$
(iii) $a^{2}+2 a b+b^{2}$
(iv) $a^{3}-b^{3}$
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Ask Chatterbot AIExercise 10.1 - Algebraic Expressions | NCERT | Mathematics | Class 7
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of $z$ from $y$.
(ii) One-half of the sum of numbers $x$ and $y$.
(iii) The number $z$ multiplied by itself.
(iv) One-fourth of the product of numbers $p$ and $q$.
(v) Numbers $x$ and $y$ both squared and added.
(vi) Number 5 added to three times the product of numbers $m$ and $n$.
(vii) Product of numbers $y$ and $z$ subtracted from 10.
(viii) Sum of numbers $a$ and $b$ subtracted from their product.
Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.
(a) $x-3$
(b) $1+x+x^{2}$
(c) $y-y^{3}$
(d) $5 x y^{2}+7 x^{2} y$
(e) $-a b+2 b^{2}-3 a^{2}$
Identify terms and factors in the expressions given below:
(a) $-4 x+5$
(b) $-4 x+5 y$
(c) $5 y+3 y^{2}$
(d) $x y+2 x^{2} y^{2}$
(e) $p q+q$
(f) $1.2 a b-2.4 b+3.6 a$
(g) $\frac{3}{4} x+\frac{1}{4}$
(h) $0.1 p^{2}+0.2 q^{2}$
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Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) $5-3 t^{2}$
(ii) $1+t+t^{2}+t^{3}$
(iii) $x+2 x y+3 y$
(iv) $100 m+1000 n$
(v) $-p^{2} q^{2}+7 p q$
(vi) $1.2 a+0.8 b$
(vii) $3.14 r^{2}$
(viii) $2(l+b)$
(ix) $0.1 y+0.01 y^{2}$
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Identify terms which contain $x$ and give the coefficient of $x$.
(i) $y^{2} x+y$
(ii) $13 y^{2}-8 y x$
(iii) $x+y+2$
(iv) $5+z+z x$
(v) $1+x+x y$
(vi) $12 x y^{2}+25$
(vii) $7 x+x y^{2}$
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Identify terms which contain $y^{2}$ and give the coefficient of $y^{2}$.
(i) $8-x y^{2}$
(ii) $5 y^{2}+7 x$
(iii) $2 x^{2} y-15 x y^{2}+7 y^{2}$
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Classify into monomials, binomials and trinomials.
(i) $4 y-7 z$
(ii) $y^{2}$
(iii) $x+y-x y$
(iv) 100
(v) $a b-a-b$
(vi) $5-3 t$
(vii) $4 p^{2} q-4 p q^{2}$
(viii) $7 m n$
(ix) $z^{2}-3 z+8$
(x) $a^{2}+b^{2}$
(xi) $z^{2}+z$
(xii) $1+x+x^{2}$
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State whether a given pair of terms is of like or unlike terms.
(i) 1,100
(ii) $-7 x, \frac{5}{2} x$
(iii) $-29 x,-29 y$
(iv) $14 x y, 42 y x$
(v) $4 m^{2} p, 4 m p^{2}$
(vi) $12 x z, 12 x^{2} z^{2}$
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Identify like terms in the following:
(a) $-x y^{2},-4 y x^{2}, 8 x^{2}, 2 x y^{2}, 7 y,-11 x^{2},-100 x,-11 y x, 20 x^{2} y$, $-6 x^{2}, y, 2 x y, 3 x$
(b) $10 p q, 7 p, 8 q,-p^{2} q^{2},-7 q p,-100 q,-23,12 q^{2} p^{2},-5 p^{2}, 41,2405 p, 78 q p$, $13 p^{2} q, q p^{2}, 701 p^{2}$
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Ask Chatterbot AIExercise 10.2 - Algebraic Expressions | NCERT | Mathematics | Class 7
If $m=2$, find the value of:
(i) $m-2$
(ii) $3 m-5$
(iii) $9-5 m$
(iv) $3 m^{2}-2 m-7$
(v) $\frac{5 m}{2} 4$
Sure, let's evaluate each expression given $m = 2$:
(i) $m - 2 = 2 - 2$
(ii) $3m - 5 = 3(2) - 5$
(iii) $9 - 5m = 9 - 5(2)$
(iv) $3m^2 - 2m - 7 = 3(2)^2 - 2(2) - 7$
(v) $\frac{5m}{2} \cdot 4 = \frac{5(2)}{2} \cdot 4$
Now, calculating the values:
(i) $m - 2 = 2 - 2 = 0$
(ii) $3m - 5 = 3(2) - 5 = 6 - 5 = 1$
(iii) $9 - 5m = 9 - 5(2) = 9 - 10 = -1$
(iv) $3m^2 - 2m - 7 = 3(2)^2 - 2(2) - 7 = 3(4) - 4 - 7 = 12 - 4 - 7 = 1$
(v) $\frac{5m}{2} \cdot 4 = \frac{5(2)}{2} \cdot 4 = \frac{10}{2} \cdot 4 = 5 \cdot 4 = 20$
Thus, the values are:
(i) $0$
(ii) $1$
(iii) $-1$
(iv) $1$
(v) $20$
If $p=-2$, find the value of:
(i) $4 p+7$
(ii) $-3 p^{2}+4 p+7$
(iii) $-2 p^{3}-3 p^{2}+4 p+7$
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Find the value of the following expressions, when $x=-1$ :
(i) $2 x-7$
(ii) $-x+2$
(iii) $x^{2}+2 x+1$
(iv) $2 x^{2}-x-2$
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If $a=2, b=-2$, find the value of:
(i) $a^{2}+b^{2}$
(ii) $a^{2}+a b+b^{2}$
(iii) $a^{2}-b^{2}$
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When $a=0, b=-1$, find the value of the given expressions:
(i) $2 a+2 b$
(ii) $2 a^{2}+b^{2}+1$
(iii) $2 a^{2} b+2 a b^{2}+a b$
(iv) $a^{2}+a b+2$
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Simplify the expressions and find the value if $x$ is equal to 2
(i) $x+7+4(x-5)$
(ii) $3(x+2)+5 x-7$
(iii) $6 x+5(x-2)$
(iv) $4(2 x-1)+3 x+11$
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Simplify these expressions and find their values if $x=3, a=-1, b=-2$.
(i) $3 x-5-x+9$
(ii) $2-8 x+4 x+4$
(iii) $3 a+5-8 a+1$
(iv) $10-3 b-4-5 b$
(v) $2 a-2 b-4-5+a$
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(i) If $z=10$, find the value of $z^{3}-3(z-10)$.
(ii) If $p=-10$, find the value of $p^{2}-2 p-100$
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What should be the value of $a$ if the value of $2 x^{2}+x-a$ equals to 5 , when $x=0$ ?
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Simplify the expression and find its value when $a=5$ and $b=-3$.
$ 2\left(a^{2}+a b\right)+3-a b$ show steps
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Ask Chatterbot AIExtra Questions - Algebraic Expressions | NCERT | Mathematics | Class 7
What should be the value of a, if the value of $2x^{2} + 6a - 5x + 10$ is 25, when $x = 1$?
A) 6
B) 3
C) -3
D) -6
To solve for the value of $a$ in the expression $2x^{2} + 6a - 5x + 10 = 25$ when $x = 1$, substitute $x = 1$ into the equation:
$$ 2(1)^2 + 6a - 5(1) + 10 = 25 $$
Simplify the left side of the equation:
$$ 2 + 6a - 5 + 10 = 25 $$
Combine like terms:
$$ 6a + 7 = 25 $$
To isolate $a$, subtract 7 from both sides:
$$ 6a = 25 - 7 $$
$$ 6a = 18 $$
Divide by 6 to solve for $a$:
$$ a = \frac{18}{6} = 3 $$
Therefore, the value of $a$ that satisfies the given condition is $a = 3$. The correct answer is:
Option B: 3
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$15 - (6 + 6 \times 6) \div (9 + 5) = ?$
A) 12
B) 24
C) 18
D) $\quad 28$
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