How to subtract the algebraic expression ?
Step 1 :
Write all the expressions into brackets and put the subtraction sign in between.
Step 2 :
Combine all the like terms together from all the expressions and rewrite them in a single expression.
Step 3 :
Add or subtract numerical coefficients of all the like terms followed by the common variable.
Step 4 :
Rewrite the simplified expression, and make sure all the terms in the final answer are unlike terms.
Subtract :
Problem 1 :
14x2 – 12x – 6 from the sum of 2x2 – 3x + 11 and 7x2 – 3x – 4.
Solution :
Let,
a = 2x2 – 3x + 11
b = 7x2 – 3x – 4
c = 14x2 – 12x – 6
The sum of a + b = (2x2 – 3x + 11) + (7x2 – 3x – 4)
By combining like terms ,
= (2x2 + 7x2) + (-3x – 3x) + (11 – 4)
a + b = 9x2 - 6x + 7
(a + b) – c = (9x2 - 6x + 7) – (14x2 – 12x – 6)
= 9x2 – 6x + 7 – 14x2 + 12x + 6
By combining like terms ,
= (9x2 – 14x2) + (-6x + 12x) + (7 + 6)
= -5x2 + 6x + 13
So, the answer is -5x2 + 6x + 13.
Problem 2 :
2x3 + 7x2 – 4x – 13 from the sum of 17x3 – 12x + 11 and x3 + 5.
Solution :
Let,
a = 17x3 – 12x + 11
b = x3 + 5
c = 2x3 + 7x2 – 4x – 13
The sum of a + b = (17x3 – 12x + 11) + (x3 + 5)
By combining like terms,
= (17x3 + x3) + (-12x) + (11 + 5)
a + b = 18x3 – 12x + 16
(a + b) – c = (18x3 – 12x + 16) – (2x3 + 7x2 – 4x – 13)
= 18x3 – 12x + 16 – 2x3 – 7x2 + 4x + 13
By combining like terms,
= (18x3 – 2x3) – (7x2) + (-12x + 4x) + (16 + 13)
= 16x3 – 7x2 – 8x + 29
So, the answer is 16x3 – 7x2 – 8x + 29.
Problem 3 :
The sum of w2 – 10w + 25 and 3w2 – 7w from the product of 4 and 2 – 5w.
Solution :
Let,
a = w2 – 10w + 25
b = 3w2 – 7w
c = 4
d = 2 - 5w
The sum of a + b = (w2 – 10w + 25) + (3w2 – 7w)
By combining like terms,
= (w2 + 3w2) + (-10w – 7w) + 25
a + b = 4w2 - 17w + 25
The product of c and d = 4 × (2 – 5w)
= 8 – 20w
(c × d) – (a + b) = (8 – 20w) - (4w2 - 17w + 25)
= 8 - 20w - 4w2 + 17w - 25
By combining like terms,
= (-4w2) + (-20w + 17w) + (8 - 25)
= -4w2 – 3w - 17
So, the answer is -4w2 – 3w – 17.
Problem 4 :
The product of 3 and 6w2 – 7w + 1 from the product of -2 and -3 – 7w.
Solution :
Let,
a = 3
b = 6w2 – 7w + 1
c = -2
d = -3 – 7w
The product of a and b = 3 x (6w2 – 7w + 1)
= 18w2 – 21w + 3
The product of c and d = -2 x (-3 – 7w)
= 6 + 14w
(c x d) – (a x b) = (6 + 14w) – (18w2 – 21w + 3)
= (6 + 14w) – (18w2 – 21w + 3)
= 6 + 14w – 18w2 + 21w – 3
By combining like terms ,
= -18w2 + (14w + 21w) + (6 – 3)
= -18w2 + 35w + 3
So, the answer is -18w2 + 35w + 3.
Simplify :
Problem 5 :
-2 {3a – 4[a – (2 + a)] }
Solution :
Given, -2 {3a – 4[a – (2 + a)] }
= -2 {3a – 4[a –2 – a] }
= -2 {3a – 4a + 8 + 4a}
= -6a + 8a – 16 - 8a
= -6a - 16
Problem 6 :
5 {3c – [d – 2(c + d)] }
Solution :
Given, 5 {3c – [d – 2(c + d)] }
= 5 {3c – [d – 2c - 2d] }
= 5 {3c – d + 2c + 2d}
= 15c – 5d + 10c + 10d
= 25c + 5d
Problem 7 :
-3a(2 + b) – 18a(b + 1)
Solution :
Given, -3a(2 + b) – 18a(b + 1)
= -6a – 3ab – 18ab – 18a
= -24a – 21ab
Problem 8 :
(-4xy2 – 16xy) [a(3y +2) – 2a(y – 1)]
Solution :
Given, (-4xy2 – 16xy) [a(3y +2) – 2a(y – 1)]
= (-4xy2 – 16xy) (3ay + 2a – 2ay + 2a)
= (-4xy2 – 16xy) (ay + 4a)
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