S.chand publication New Learning Composite mathematics solution of class 7 Chapter 5 Algebraic Expression Exercise 5C

 Exercise 5C

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Q1 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 1

Subtract

(a) 2x from 7x

Sol : 5x

(b) -5a from -2a

Sol : -2a-(-5a)

=3a

(c) 3b² from -5b²

Sol :

=-8b²

(d) -2xy from 0

Sol :

=2xy

(e) -8cd from 8cd

Sol :

=8cd+8cd

=16cd

(f) 3(x + y) from 4(x + y)

Sol :

=4x+4y-3x-3y

=x+y

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Q2 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 2

Subtract the lower expression from the upper expression.

(a) (7a + 5) – (2a + 1)

Sol :

$\begin{array}{r}7a+5 \\ 2a+1 \\ -\phantom{2a}-\phantom{1} \\ \hline 5a+4 \end{array}$

(b) (9x² + 3y²) – (5x² + y²)

Sol :

$\begin{array}{r}9x^2+3y^2\\ 5x^2+y^2 \\ -\phantom{5x^2}-\phantom{y^2} \\ \hline 4x^2+2y^2 \end{array}$

(c) (5ab – 7bc) – (2ab + bc)

Sol :

$\begin{array}{r}5ab-7bc\\2ab+bc\\ -\phantom{2ab}-\phantom{bc} \\ \hline 3ab-8bc\end{array}$

(d) (9x²y – 11) – (-2x²y – 5)

Sol :

$\begin{array}{r}9x^2y-11\\+2x^2y+5\\ \hline 11x^2y-6\end{array}$

(e) (2m³ – 9n²) – (4m³ – 11n²)

Sol :

$\begin{array}{r}2m^3-9n^2\\ 4m^3+11n^2\\ \hline -2m^3+2n^2\end{array}$

(f) (4x²y – 5xy²) – (4x²y – 5xy²)

Sol :

$\begin{array}{r}4x^2y-5xy^2\\ 4x^2y+5xy^2\\ \hline 0\end{array}$

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Q3 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 3

Arrange the following in columns and subtract.

(a) 7p + 2q + 5c from 9p + 4q + 7c

Sol :

$\begin{array}{r}9p + 4q + 7c \\ 7p+2q+5c\\ -\phantom{7p}-\phantom{2q}-\phantom{5c} \\ \hline 2p+2q+2c\end{array}$

(b) 3x² – 8xy – 9y² from 3x² – 8xy – 9y²

Sol :

$\begin{array}{r}3x^2-8xy-9y^2 \\ 3x^2+8xy+9y^2\\ -\phantom{3x^2}-\phantom{8xy}-\phantom{9y^2} \\\hline 0\end{array}$

(c) 8x² – 9x + 5 from 4x³ – 3x² + 7x + 11

Sol :

$\begin{array}{r}4x^3-3x^2+7x+11\\ 8x^2+9x+5\\ -\phantom{8x^2}-\phantom{9x}-\phantom{5} \\ \hline 4x^3-11x^2+16x+6\end{array}$

(d) -2p³ + 7p² – 20 + 3p from 0

Sol :

=2p³-7p²+20-3p

(e) 4ax² + 7bx – 9t + 6 from 8ax² – 2bx + 10t -4

Sol :

$\begin{array}{r} 8ax^2-2bx+10x-4 \\ 4ax^2+7bx+9x+6\\ -\phantom{4ax^2}-\phantom{7bx}-\phantom{9x}-\phantom{6} \\ \hline 4ax^2-9bx+19x-10\end{array}$

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Q4 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 4

Subtract the following without writing in vertical form.

(a) 2x + 3y from 7x + 9y

Sol : 5x+6y

(b) -2x – y from 2x + y

Sol : 4x+2y

(c) – 5m² + 4mn – n² from 2m² + 8mn + 3n²

Sol : 2m² + 8mn + 3n²-(– 5m² + 4mn – n²)

(d) – 2p³ + 4p² – 7 – p from 16 – 8p

Sol : 16-8p+2p³–4p²+7+p

(e) 4xy – 3x²y + 7xy² from 27 – 7xy² + 11xy

Sol : 27 – 7xy² + 11xy-(4xy – 3x²y + 7xy²)

=23-7p+2p³-4p²

(f) The sum of x² – 2xy + y² and x² + 3xy + y² from x² – 6xy + 4y²

Sol :

=2x²+xy+2y²

∴x²-6xy+4y²-2x²-xy-2y²

=-x²-7xy+2y²

(g) The sum of 9b² – 3c² and 2b² + bc – 2c² from the sum of 2b² – 2bc – c² and c² + 2bc – b²

Sol :

2b² – 2bc – c² and c² + 2bc – b²-(9b² – 3c² and 2b² + bc – 2c²)

=b²-(11b²-5c²+bc)

=b²-11b²+5c²-bc

=-10b²+5c²-bc

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Q5 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 5

Simplify:

(a) 3x² – 5x + 7 – 5x² – 11 + 8x + 20 + 9x² – 6x

Sol :

=7x²-3x+16

(b) 5x³ – 8 + 7x²y – 7xy + 10xy² + 11 – 2x³ – 5x²y + 9xy – 6xy²

Sol :

=3x³+3+2x²y+2xy+4xy²

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Q6 | Ex-5C|Class 8 |S.Chand |Composite maths | Algebraic Expression |Ch-6 |myhelper

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Question 6

The area of a square 4x² – 2xy – 6y² square units. A triangle inside has an area of -5xy + 4y² – 3x² square units. Find the area of the shaded region.

Sol :

Area of shaded region=(4x² – 2xy – 6y²+5xy-4y²+3x²) sq unit

=(7x²+3xy-10y²)