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Textbook | NCERT |

Class | Class 7 |

Subject | Maths |

Chapter | Chapter 7 |

Chapter Name | Algebraic Expressions |

Exercise | Ex 7.2 |

Table of Contents

**RD Sharma Solutions for Class 7 Chapter 7 Decimals** **Ex 7.2 Download PDF**

**Chapter 7: Algebraic Expressions Exercise – 7.2**

**Question: 1**

Add the following:

(i) 3x and 7x

(ii) -5xy and 9xy

**Solution:**

We have

(i) 3x + 7x = (3 + 7) x = 10x

(ii) -5xy + 9xy = (-5 + 9)xy = 4xy

**Question: 2**

Simplify each of the following:

(i) 7x^{3}y +9yx^{3}

(ii) 12a^{2}b + 3ba^{2}

**Solution:**

Simplifying the given expressions, we have

(i) 7x^{3}y + 9yx^{3} = (7 + 9)x^{3}y = 16x^{3}y

(ii) 12a^{2}b + 3ba^{2 }= (12 + 3)a^{2}b =15a^{2}b

**Question: 3**

Add the following:

(i) 7abc, -5abc, 9abc, -8abc

(ii) 2x^{2}y, – 4x^{2}y, 6x^{2}y, -5x^{2}y

**Solution:**

Adding the given terms, we have

(i) 7abc + (-5abc) + (9abc) + (-8abc)

= 7abc – 5abc + 9abc – 8abc

= (7 – 5 + 9 – 8)abc

= (16 – 13)abc

= 3abc

(ii) 2x^{2}y +(-4x^{2}y) + (6x^{2}y) + (-5x^{2}y)

= 2x^{2}y – 4x^{2}y + 6x^{2}y – 5x2y

= (2- 4 + 6 – 5) x 2y

= (8 – 9) x 2y

= -x^{2}y

**Question: 4**

Add the following expressions:

(i) x^{3} -2x^{2}y + 3xy^{2}– y^{3}, 2x^{3}– 5xy^{2} + 3x^{2}y – 4y^{3}

(ii) a^{4} – 2a^{3}b + 3ab^{3} + 4a^{2}b^{2 }+ 3b^{4}, – 2a^{4} – 5ab^{3} + 7a^{3}b – 6a^{2}b^{2 }+ b^{4}

**Solution:**

Adding the given expressions, we have

(i) x^{3} -2x^{2}y + 3xy^{2}– y^{3}, 2x^{3}– 5xy^{2} + 3x^{2}y – 4y^{3}

Collecting positive and negative like terms together, we get

x^{3} +2x^{3 }– 2x^{2}y + 3x^{2}y + 3xy^{2} – 5xy^{2} – y^{3}– 4y^{3}

= 3x^{3} + x^{2}y – 2xy^{2 }– 5y^{3}

(ii) a^{4} – 2a^{3}b + 3ab^{3} + 4a^{2}b^{2 }+ 3b^{4}, – 2a^{4} – 5ab^{3} + 7a^{3}b – 6a^{2}b^{2 }+ b^{4}

a^{4} – 2a^{3}b + 3ab^{3} + 4a^{2}b^{2} + 3b^{4} – 2a^{4} – 5ab^{3 }+ 7a^{3}b – 6a^{2}b^{2} + b^{4}

Collecting positive and negative like terms together, we get

a^{4} – 2a^{4}– 2a^{3}b + 7a^{3}b + 3ab^{3} – 5ab^{3} + 4a^{2}b^{2} – 6a^{2}b^{2 }+ 3b^{4} + b^{4}

= – a^{4 }+ 5a^{3}b – 2ab^{3} – 2a^{2}b^{2 }+ 4b^{4}

**Question: 5**

Add the following expressions:

(i) 8a – 6ab + 5b, –6a – ab – 8b and –4a + 2ab + 3b

(ii) 5x^{3} + 7 + 6x – 5x^{2}, 2x^{2} – 8 – 9x, 4x – 2x^{2} + 3 x 3, 3 x 3 – 9x – x^{2} and x – x^{2} – x^{3} – 4

**Solution:**

(i) Required expression = (8a – 6ab + 5b) + (–6a – ab – 8b) + (–4a + 2ab + 3b)

Collecting positive and negative like terms together, we get

8a – 6a – 4a – 6ab – ab + 2ab + 5b – 8b + 3b

= 8a – 10a – 7ab + 2ab + 8b – 8b

= –2a – 5ab

(ii) Required expression = (5 x 3 + 7+ 6x – 5x^{2}) + (2 x 2 – 8 – 9x) + (4x – 2x^{2} + 3 x 3) + (3 x 3 – 9x-x^{2}) + (x – x^{2} – x^{3} – 4)

Collecting positive and negative like terms together, we get

5x^{3} + 3x^{3} + 3x^{3} – x^{3} – 5x^{2} + 2x^{2 }– 2x^{2}– x^{2} – x^{2} + 6x – 9x + 4x – 9x + x + 7 – 8 – 4

= 10x^{3} – 7x^{2} – 7x – 5

**Question: 6**

Add the following:

(i) x – 3y – 2z

5x + 7y – 8z

3x – 2y + 5z

(ii) 4ab – 5bc + 7ca

–3ab + 2bc – 3ca

5ab – 3bc + 4ca

**Solution:**

(i) Required expression = (x – 3y – 2z) + (5x + 7y – 8z) + (3x – 2y + 5z)

Collecting positive and negative like terms together, we get

x + 5x + 3x – 3y + 7y – 2y – 2z – 8z + 5z

= 9x – 5y + 7y – 10z + 5z

= 9x + 2y – 5z

(ii) Required expression = (4ab – 5bc + 7ca) + (–3ab + 2bc – 3ca) + (5ab – 3bc + 4ca)

Collecting positive and negative like terms together, we get

4ab – 3ab + 5ab – 5bc + 2bc – 3bc + 7ca – 3ca + 4ca

= 9ab – 3ab – 8bc + 2bc + 11ca – 3ca

= 6ab – 6bc + 8ca

**Question: 7**

Add 2x^{2} – 3x + 1 to the sum of 3x^{2} – 2x and 3x + 7.

**Solution:**

Sum of 3x^{2} – 2x and 3x + 7

= (3x^{2} – 2x) + (3x +7)

=3x^{2} – 2x + 3x + 7

= (3x^{2} + x + 7)

Now, required expression = 2x^{2 }– 3x + 1+ (3x^{2 }+ x + 7)

= 2x^{2 }+ 3x^{2} – 3x + x + 1 + 7

= 5x^{2 }– 2x + 8

**Question: 8**

Add x^{2 }+ 2xy + y^{2} to the sum of x^{2} – 3y^{2}and 2x^{2 }– y^{2} + 9.

**Solution:**

**Question: 9**

Add a^{3}+ b^{3} – 3 to the sum of 2a^{3} – 3b^{3 }– 3ab + 7 and -a^{3} + b^{3} + 3ab – 9.

**Solution:**

**Question: 10**

Subtract:

(i) 7a^{2}b from 3a^{2}b

(ii) 4xy from -3xy

**Solution:**

(i) Required expression = 3a^{2}b -7a^{2}b

= (3 -7)a^{2}b

= – 4a^{2}b

(ii) Required expression = –3xy – 4xy

= –7xy

**Question: 11**

Subtract:

(i) – 4x from 3y

(ii) – 2x from – 5y

**Solution:**

(i) Required expression = (3y) – (–4x)

= 3y + 4x

(ii) Required expression = (-5y) – (–2x)

= –5y + 2x

**Question: 12**

Subtract:

(i) 6x^{3 }−7x^{2 }+ 5x − 3 from 4 − 5x + 6x^{2} − 8x^{3}

(ii) − x^{2 }−3z from 5x^{2 }– y + z + 7

(iii) x^{3} + 2x^{2}y + 6xy^{2} − y^{3} from y^{3}−3xy^{2}−4x^{2}y

**Solution:**

**Question: 13**

From

(i) p3 – 4 + 3p^{2}, take away 5p^{2} − 3p^{3} + p − 6

(ii) 7 + x − x^{2}, take away 9 + x + 3x^{2} + 7x^{3}

(iii) 1− 5y^{2}, take away y^{3} + 7y^{2} + y + 1

(iv) x^{3} − 5x^{2} + 3x + 1, take away 6x^{2} − 4x^{3} + 5 + 3x

**Solution:**

**Question: 14**

From the sum of 3x^{2} − 5x + 2 and − 5x^{2 }− 8x + 9 subtract 4x^{2} − 7x + 9.

**Solution:**

**Question: 15**

Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7.

**Solution:**

Sum of (13x – 4y + 7z) and (–6z + 6x + 3y)

= (13x – 4y + 7z) + (–6z + 6x + 3y)

= (13x – 4y + 7z – 6z + 6x + 3y)

= (13x + 6x – 4y + 3y + 7z – 6z)

= (19x – y + z)

Sum of (6x – 4y – 4z) and (2x + 4y – 7)

= (6x – 4y – 4z) + (2x + 4y – 7)

= (6x – 4y – 4z + 2x + 4y – 7)

= (6x + 2x – 4z – 7)

= (8x – 4z – 7)

Now, required expression = (8x – 4z – 7) – (19x – y + z)

= 8x – 4z – 7 – 19x + y – z

= 8x – 19x + y – 4z – z – 7

= –11x + y – 5z – 7

**Question: 16**

From the sum of x^{2 }+ 3y^{2} − 6xy, 2x^{2} − y^{2} + 8xy, y^{2} + 8 and x^{2} − 3xy subtract −3x^{2} + 4y^{2} – xy + x – y + 3.

**Solution:**

**Question: 17**

What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7?

**Solution:**

The required expression can be got by subtracting xy – 3yz + 4zx from 4xy – 3zx + 4yz + 7.

Therefore, required expression = (4xy – 3zx + 4yz + 7) – (xy – 3yz + 4zx)

= 4xy – 3zx + 4yz + 7 – xy + 3yz – 4zx

= 4xy – xy – 3zx – 4zx + 4yz + 3yz + 7

= 3xy – 7zx + 7yz + 7

**Question: 18**

What should be subtracted from x^{2} – xy + y^{2} – x + y + 3 to obtain −x^{2 }+ 3y^{2 }− 4xy + 1?

**Solution:**

**Question: 19**

How much is x – 2y + 3z greater than 3x + 5y – 7?

**Solution:**

Required expression = (x – 2y + 3z) – (3x + 5y – 7)

= x – 2y + 3z – 3x – 5y + 7

Collecting positive and negative like terms together, we get

x – 3x – 2y + 5y + 3z + 7

= –2x – 7y + 3z + 7

**Question: 20**

How much is x^{2} − 2xy + 3y^{2 }less than 2x^{2} − 3y^{2} + xy?

**Solution:**

**Question: 21**

How much does a^{2 }− 3ab + 2b^{2 }exceed 2a^{2 }− 7ab + 9b^{2}?

**Solution:**

**Question: 22**

What must be added to 12x^{3 }− 4x^{2} + 3x − 7 to make the sum x^{3} + 2x^{2 }− 3x + 2?

**Solution:**

**Question: 23**

If P = 7x^{2} + 5xy − 9y^{2}, Q = 4y^{2} − 3x^{2} − 6xy and R = −4x^{2} + xy + 5y^{2}, show that P + Q + R = 0.

**Solution:**

**Question: 24**

If P = a^{2} − b^{2} + 2ab, Q = a^{2 }+ 4b^{2} − 6ab, R = b^{2} + b, S = a^{2 }− 4ab and T = −2a^{2} + b^{2} – ab + a. Find P + Q + R + S – T.

**Solution:**

**All Chapter RD Sharma Solutions For Class 7 Maths**

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