# Algebraic Expressions - Class 7 - Mathematics

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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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Sign up nowState 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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Sign up nowFind 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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Sign up nowFind 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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## Exercise 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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## Exercise 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