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Page No 130:

Question 1:

Can you write the algebraic expressions for these?

(i) Two added to three times a number.

(ii) Three times the sum of a number and two.

(iii) One added to the square of a number.

(iv) The square of the sum of a number and one.

(v) The sum of the third and fourth powers of a number.

(vi) The sum of the fourth powers of two numbers.

 

Answer:

(i) Let the number be x.

Three times the number = 3x

Two added to three times the number = 3x + 2

(ii) Let the number be x.

Sum of the number and two = x + 2

Three times the sum of the number and two = 3(x + 2)

(iii) Let the number be x.

Square of the number = x2

One added to the square of the number = x2 + 1

(iv) Let the number be x.

Sum of the number and one = x + 1

Square of the sum of the number and one = (x + 1)2

(v) Let the number be x.

Third power of the number = x3

Fourth power of the number = x4

Sum of the third and fourth powers of the number = x3 + x4

(vi) Let the first number be x and the second number be y.

Fourth power of the first number = x4

Fourth power of the second number = y4

Sum of the fourth powers of the two numbers = x4+ y4

Page No 130:

Question 2:

Now can you write the meaning of the expressions below in ordinary language?

(i)

(ii)

(iii)

(iv)

(v) x + y + 2

(vi)

(vii) ab + 1

(viii) (a + 1) (b + 1)

 

Answer:

(i)

The given expression can be written as one added to half of a number.

(ii)

The given expression can be written as half of the sum of a number and one.

(iii)

The given expression can be written as one added to the square root of a number.

(iv)

The given expression can be written as the square root of the sum of a number and one.

(v) x + y + 2

The given expression can be written as two added to the sum of two numbers.

(vi)

The given expression can be written as the sum of the square roots of two numbers.

(vii) ab + 1

The given expression can be written as one added to the product of two numbers.

(viii) (a + 1) (b + 1)

The given expression can be written as the product of the successors of two numbers.



Page No 132:

Question 1:

Now can’t you simplify these?

(i) 2x + (3x + 1)

(ii) x + (2x + 3)

(iii) (x + 2) + (2x + 1)

(iv) (x + 1) + (x + y)

(v) (3x + 2y) + (x + y)

(vi) (3x + 2y) + (2x + 3y)

 

Answer:

(i) 2x + (3x + 1)

= (2x + 3x) + 1

= 5x + 1

(ii) x + (2x + 3)

= (x + 2x) + 3

= 3x + 3

= 3(x + 1)

(iii) (x + 2) + (2x + 1)

= (x + 2x) + (2 + 1)

= 3x + 3

= 3(x + 1)

(iv) (x + 1) + (x + y)

= (x + x) + 1 + y

= 2x + y + 1

(v) (3x + 2y) + (x + y)

= (3x + x) + (2y + y)

= 4x + 3y

(vi) (3x + 2y) + (2x + 3y)

= 3x + 2y + 2x + 3y

= (3x + 2x) + (2y + 3y)

= 5x + 5y

= 5(x + y)



Page No 133:

Question 1:

Now can you simplify these?

(i) (x + 4) + (x − 2)

(ii) (2x + 3) + (x − 1)

(iii) (x + 1) + (x − 1)

(iv) (5x + 6y) + (2x − 3y)

(v) (x + y) + (x y)

 

Answer:

(i) (x + 4) + (x 2)

= (x + 4 + x) 2 [for any three numbers x, y, z, with y > z, x + (y z) = (x + y) z]

= (2x + 4) 2

= 2x + (4 − 2)

= 2x + 2

= 2(x + 1)

(ii) (2x + 3) + (x 1)

= (2x + 3 + x) 1 [for any three numbers x, y, z, with y > z, x + (y z) = (x + y) z]

= (3x + 3) 1

= 3x + (3 − 1)

= 3x + 2

(iii) (x + 1) + (x 1)

= (x + 1 + x) 1 [for any three numbers x, y, z, with y > z, x + (y z) = (x + y) z]

= (2x + 1) 1

= 2x + (1 − 1)

= 2x + 0

= 2x

(iv) (5x + 6y) + (2x 3y)

= (5x + 6y + 2x) 3y [for any three numbers x, y, z, with y > z, x + (y z) = (x + y) z]

= (7x + 6y) 3y

= 7x + (6y − 3y)

= 7x + 3y

(v) (x + y) + (x y)

= (x + y + x) y [for any numbers x, y, z, with y > z, x + (y z) = (x + y) z]

= (2x + y) y

= 2x + (yy)

= 2x + 0

= 2x



Page No 135:

Question 1:

Now can’t you simplify these?

(i) (2x − 1) + (x − 2)

(ii) (5x − 6y) + (2x − 3y)

(iii) (2x − 3y) + (3x − 2y)

(iv) (x y) + (x y)

 

Answer:

(i) (2x 1) + (x 2)

= 2x 1 + x 2

= (2x + x) 1 2

= 3x (1 + 2)

= 3x 3

= 3(x 1)

(ii) (5x 6y) + (2x 3y)

= 5x 6y + 2x 3y

= (5x + 2x) 6y 3y

= 7x (6y + 3y)

= 7x 9y

(iii) (2x 3y) + (3x 2y)

= 2x 3y + 3x 2y

= (2x + 3x) 3y 2y

= 5x (3y + 2y)

= 5x 5y

= 5(xy)

(iv) (x y) + (x y)

= x y + x y

= (x + x) y y

= 2x (y + y)

= 2x 2y

= 2(xy)



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