Find the sum of:
3a+4b+7c,−5a+3b−6c and 4a−2b−4c
Answer
Solving,
+3a−5a4a2a+4b+3b−2b+5b+7c−6c−4c−3c
Hence, the required sum = 2a+5b−3c.
Find the sum of:
2x2+xy−y2,−x2+2xy+3y2 and 3x2−10xy+4y2
Answer
Solving,
+2x2−x23x24x2+xy+2xy−10xy−7xy−y2+3y2+4y2+6y2
Hence, the required sum = 4x2−7xy+6y2.
Find the sum of:
x2−x+1,−5x2+2x−2 and 3x2−3x+1
Answer
Solving,
+x2−5x23x2−x2−x+2x−3x−2x+1−2+1+0
Hence, the required sum = −x2−2x.
Find the sum of:
a2−ab+bc,2ab+bc−2a2 and −3bc+3a2+ab
Answer
Solving,
+a2−2a23a22a2−ab+2ab+ab+2ab+bc+bc−3bc−bc
Hence, the required sum = 2a2+2ab−bc.
Find the sum of:
4x2+7−3x,4x−x2+8 and −10+5x−2x2
Answer
Solving,
+4x2−x2−2x2x2−3x+4x+5x+6x+7+8−10+5
Hence, the required sum = x2+6x+5.
Find the sum of:
3x+4xy−y2,xy−4x+2y2 and 3y2−xy+6x
Answer
Solving,
+3x−4x6x5x+4xy+xy−xy+4xy−y2+2y2+3y2+4y2
Hence, the required sum = 5x+4xy+4y2.
Add the following expressions:
−17x2−2xy+23y2,−9y2+15x2+7xy and 13x2+3y2−4xy
Answer
Solving,
+−17x215x213x211x2−2xy+7xy−4xy+xy+23y2−9y2+3y2+17y2
Hence, the required sum = 11x2+xy+17y2.
Add the following expressions:
−x2−3xy+3y2+8,3x2−5y2−3+4xy and −6xy+2x2−2+y2
Answer
Solving,
+−x23x22x24x2−3xy+4xy−6xy−5xy+3y2−5y2+y2−y2+8−3−2+3
Hence, the required sum = 4x2−5xy−y2+3.
Add the following expressions:
a3−2b3+a,b3−2a3+b and −2b+2b3−5a+4a3
Answer
Solving,
+a3−2a34a33a3−2b3+b3+2b3+b3+a−5a−4a+b−2b−b
Hence, the required sum = 3a3+b3−4a−b.
Evaluate:
3a−(a+2b)
Answer
Solving,
+3a+a−+2a+2b−−2b
Hence, the value of the given expression = 2a−2b.
Evaluate:
(5x−3y)−(x+y)
Answer
Solving,
+5x+x−+4x−3y+y−−4y
Hence, the value of the given expression = 4x−4y.
Evaluate:
(8a+15b)−(3b−7a)
Answer
Solving,
+8a−7a++15a+15b+3b−+12b
Hence, the value of the given expression = 15a+12b.
Evaluate:
(8x+7y)−(4y−3x)
Answer
Solving,
+8x−3x++11x+7y+4y−+3y
Hence, the value of the given expression = 11x+3y.
Evaluate:
7−(4a−5)
Answer
Solving,
⇒7−(4a−5)⇒7−4a+5⇒12−4a.
Hence, the value of the given expression = 12−4a.
Subtract:
5a−3b+2c from a−4b−2c
Answer
Solving,
+a+5a−−4a−4b−3b+−b−2c+2c−−4c
Hence, the required difference = −4a−b−4c.
Subtract:
4x−6y+3z from 12x+7y−21z
Answer
Solving,
+12x+4x−+8x+7y−6y++13y−21z+3z−−24z
Hence, the required difference = 8x+13y−24z.
Subtract:
5−a−4b+4c from 5a−7b+2c
Answer
Solving,
+5a−a++6a−7b−4b+−3b+2c+4c−−2c+5−−5
Hence, the required difference = 6a−3b−2c−5.
Subtract:
−8x−12y+17z from x−y−z
Answer
Solving,
+x−8x++9x−y−12y++11y−z+17z−−18z
Hence, the required difference = 9x+11y−18z.
Subtract:
2ab+cd−ac−2bd from ab−2cd+2ac+bd
Answer
Solving,
+ab+2ab−−ab−2cd+cd−−3cd+2ac−ac++3ac+bd−2bd++3bd
Hence, the required difference = −ab−3cd+3ac+3bd.
Take −ab+bc−ca from bc−ca+ab.
Answer
Solving,
+ab−ab++2ab+bc+bc−−ca−ca+
Hence, the required difference = 2ab.
Take 5x+6y−3z from 3x+5y−4z.
Answer
Solving,
+3x+5x−−2x+5y+6y−−y−4z−3z+−z
Hence, the required difference = −2x−y−z.
Take 2−3p+q−r from 21p−31q−23r.
Answer
Solving,
⇒(21p−31q−23r)−(−23p+q−r)⇒21p−31q−23r+23p−q+r⇒21p+23p−31q−q−23r+r⇒(21+23)p+(−31−1)q+(−23+1)r⇒21+3p+3−1−3q+2−3+2r⇒24p−34q−21r⇒2p−34q−21r.
Hence, the required difference = 2p−34q−21r.
Take 1−a+a2 from a2+a+1.
Answer
Solving,
+a2+a2−+a−a++2a+1+1−
Hence, the required difference = 2a.
From the sum of x+y−2z and 2x−y+z, subtract x+y+z.
Answer
Sum of x+y−2z and 2x−y+z,
+x2x3x+y−y0−2z+z−z
Now, subtracting x+y+z from this sum,
+3x+x−+2x0+y−−y−z+z−−2z
Hence, the required difference = 2x−y−2z.
From the sum of 3a−2b+4c and 3b−2c, subtract a−b−c.
Answer
Sum of 3a−2b+4c and 3b−2c,
+3a3a−2b+3b+b+4c−2c+2c
Now, subtracting a−b−c from this sum,
+3a+a−+2a+b−b++2b+2c−c++3c
Hence, the required difference = 2a+2b+3c.
Subtract x−2y−z from the sum of 3x−y+z and x+y−3z.
Answer
Sum of 3x−y+z and x+y−3z,
+3xx4x−y+y0+z−3z−2z
Now, subtracting x−2y−z from this sum,
+4x+x−+3x0−2y++2y−2z−z+−z
Hence, the required difference = 3x+2y−z.
Subtract the sum of x+y and x−z from the sum of x−2z and x+y+z.
Answer
Sum of x−2z and x+y+z,
+xx2x+y+y−2z+z−z
Sum of x+y and x−z,
+xx2x+y+y−z−z
Now, subtracting the second sum from the first sum,
+2x+2x−0+y+y−0−z−z+0
Hence, the required difference = 0.
