Question

Add the following algebraic expressions.

b. x^2 + 5x + 4, 5x^2y– 8x​

Answer 1

Answer: the answer is

these questions will help u in your  examination please do them

(i) 5x, 7x, −6x

(ii) 35x,23x,−45x

(iii) 5a2b, −8a2b, 7a2b

(iv) 34x2,5x2,−3x2,−14x2

(v) x − 3y + 4z, y − 2x − 8z, 5x − 2y − 3z

(vi) 2x2 − 3y2, 5x2 + 6y2, − 3x2 − 4y2

(vii) 5x − 2x2 − 8, 8x2 − 7x − 9, 3 + 7x2 − 2x

(viii) 23a−45b+35c,−34a−52b+23c,52a+74b−56c

(ix) 85x+117y+94xy,−32x−53y−95xy

(x) 32x3−14x2+53,−54x3+35x2−x+15,−x2+38x−815

ANSWER:

(i)

 5x + 7x + (-6x)

= 5x + 7x -6x

= 6x

(ii)

35x +23x +−45x=9x +10x −12x15=7x15

(iii)  

5a2b +( −8a2b)  + 7a2b

= 5a2b − 8a2b + 7a2b

4a2b

(iv)

 34x2 + 5x2+ (−3x2 ) + (−14x2)=34x2 − 14x2 + 5x2−3x2=12x2 + 2x2 = 52x2

(v) Collecting like terms and adding them:

x − 3y + 4z + y − 2x − 8z + 5x − 2y − 3z

= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z        

= 4x -4y -7z

(vi) Collecting like terms and adding them:

2x2 − 3y2 + 5x2 + 6y2 + (− 3x2 − 4y2)

= 2x2 + 5x2 − 3x2 − 3y2 +6y2 −4y2= 4x2 −y2                    

(vii) Collecting like terms and adding them:

5x − 2x2 − 8 +  8x2 − 7x − 9 +  3 + 7x2 − 2x

= −2x2 +8x2 + 7x2 + 5x − 7x − 2x −8 −9 + 3= 13x2 −4x −14      

(viii) Collecting like terms and adding them:

23a−45b+35c +(−34a −52b+23c )+ 52a+74b− 56c   b −52b +74b +35c +23c − 56c =(8 −9 +30)a12 + (−16 − 50 +35)b20 + (18 +20 −25)c30=2912a − 3120b + 1330c

(ix) Collecting like terms and adding them:

85x+ 117y+94xy + (− 32x− 53y−95xy)=85x − 32x+ 117y − 53y +94xy −95xy = 110x − 221y + 920xy

(x) Collecting like terms and adding them:

32x3−14x2 +53+(− 54x3+35x2− x+15)+(− x2  +38x−815)= 32x3 − 54x3 −14x2 +35x2− x2  − x +38x +53+15−815=14x3 − 1320x2 −58x +43x+117y+94xy,−32x−53y−9

Page No 99:

Question 2:

Subtract:

(i) −8xy from 7xy

(ii) x2 from − 3x2

(iii) (x − y) from (4y − 5x)

(iv) (a2 + b2 − 2ab) from (a2 + b2 + 2ab)

(v) (x2 − y2) from (2x2 − 3y2 + 6xy)

(vi) (x − y + 3z) from (2z − x − 3y)

ANSWER:

(i) 7xy- (-8xy)

= 7xy+ 8xy

= 15xy

(ii)  - 3x2 - x2

= -4x2

(iii)  (4y - 5x) - (x- y)

= 4y - 5x - x + y

= 5y - 6x

(iv) (a2 + b2 + 2ab) - (a2 + b2 − 2ab)

= a2 −a2 +b2 −b2 + 2ab + 2ab    (Collecting like terms and adding them)

= 4ab

(v) (2x2 − 3y2 + 6xy) -  (x2 − y2)

2x2 − x2 − 3y2 + y2 +6xy=x2 −2y2 +6xy     (Collecting like terms and adding them)

(vi)  (2z -x -3y) - (x - y +3z)

= 2z -3z -x -x -3y +y       (Collecting like terms and adding them)

= -z -2x - 2y  

Page No 99:

Question 3:

Subtract (2a − 3b + 4c) from the sum of (a + 3b − 4c), (4a − b + 9c) and (−2b + 3c − a).

ANSWER:

(a + 3b − 4c) + (4a − b + 9c) + (−2b + 3c − a)

= a + 4a - a + 3b -b -2b -4c +9c + 3c

= 4a + 8c

Now,  (4a + 8c ) - (2a − 3b + 4c)

= 4a - 2a + 3b + 8c - 4c

= 2a + 3b + 4c

Step-by-step explanation: