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Add the following algebraic expressions:
Subtract:
(i) – 5xy from 12xy
(ii) 2a2 from -7a 2
(iii) 2a – b from 3a – 5b
(i) 12xy – (–5xy)
= 12xy + 5xy = 17xy
(ii) –7a2 – (2a2)
= –7a2 – 2a2 = –9a2
(iii) (3a – 5b) – (2a – b)
= (3a – 5b) – 2a + b
= 3a – 5b – 2a + b
= 3a – 2a – 5b + b = a – 4b
Take away:
Subtract 3x – 4y – 7z from the sum of x – 3y + 2z and –4x + 9y – 11z
First add the expressions x – 3y + 2z and –4x + 9y – 11z we get:
(x – 3y + 2z ) + (–4x + 9y – 11z)
= x – 3y + 2z – 4x + 9y – 11z
= x – 4x – 3y + 9y + 2z – 11z (Collecting like terms)
= –3x + 6y – 9z (Combining like terms)
Now, Subtracting the expression 3x – 4y – 7z from the above sum, we get:
(–3x + 6y – 9z) – (3x – 4y – 7z)
= – 3x + 6y – 9z – 3x + 4y + 7z
= – 3x – 3x + 6y + 4y – 9z + 7z (Collecting like terms)
= – 6x + 10y – 2z (Combining like terms)
Thus, the answer is – 6x + 10y – 2z.
Subtract the sum of 3l – 4m – 7n2 and 2l + 3m – 4n2 from the sum of 9l + 2m – 3n2 and –3l + m + 4n2.
We have to subtract the sum of (3l – 4m – 7n2) and (2l + 3m – 4n2) from the sum of (9l + 2m – 3n2) and (–3l + m + 4n2)
{(9l + 2m – 3n2) + (–3l + m + 4n2)} – {(3l – 4m – 7n2) + (2l + 3m – 4n2)}
= (9l – 3l + 2m + m – 3n2 + 4n2) – (3l + 2l – 4m + 3m – 7n2 – 4n2)
= (6l + 3m + n2) – (5l – m – 11n2) (Combining like terms inside the parenthesis)
= 6l + 3m + n2 – 5l + m + 11n2
= 6l – 5l + 3m + m + n2 + 11n2 (Collecting like terms)
= l + 4m + 12n2 (Combining like terms)
Thus, the required solution is l + 4m + 12n2.
Subtract the sum 2x – x2 + 5 and –4x – 3 + 7x2 from 5.
We have to subtract the sum of (2x – x2 + 5) and (–4x – 3 + 7x2) from 5.
5 – {(2x – x2 + 5) + (–4x – 3 + 7x2)}
= 5 – (2x – 4x – x2 + 7x2 + 5 – 3)
= 5 – 2x + 4x + x2 – 7x2 – 5 + 3
= 5 – 5 + 3 – 2x + 4x + x2 – 7x2 (Collecting like terms)
= 3 + 2x – 6x2 (Combining like terms)
Thus, the answer is 3 + 2x – 6x2.
Simplify each of the following:
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Chapter 6: Algebraic Expressions and Identities...