Question

Subtract:
(i) 5a + 7b − 2c from 3a − 7b + 4c
(ii) a − 2b − 3c from −2a + 5b − 4c
(iii) 5x² − 3xy + y² from 7x² − 2xy − 4y²
(iv) 6x³ − 7x² + 5x − 3 from 4 − 5x + 6x² − 8x³
(v) x³ + 2x²y + 6xy² − y³ from y³ − 3xy² − 4x²y
(vi) −11x²y² + 7xy −6 from 9x²y² −6xy + 9
(vii) −2a + b + 6d from 5a − 2b − 3c

Answer 1

Change the sign of each term of the expression that is to be subtracted and then add.

(i) Term to be subtracted = 5a + 7b − 2c
Changing the sign of each term of the expression gives -5a -7b + 2c.
On adding:
(3a − 7b + 4c)+(-5a -7b + 2c ) = 3a − 7b + 4c-5a -7b + 2c
= (3-5)a+( − 7-7)b + (4+2)c
= -2a − 14b + 6c

(ii) Term to be subtracted = a − 2b − 3c
Changing the sign of each term of the expression gives -a +2b + 3c.
On adding:
(−2a + 5b − 4c)+(-a +2b + 3c ) = −2a + 5b − 4c-a +2b + 3c
= (−2-1)a + (5+2)b +(−4+3)c
= −3a + 7b − c

(iii) Term to be subtracted = 5x² − 3xy + y²
Changing the sign of each term of the expression gives -5x² + 3xy - y².

On adding:
(7x² − 2xy − 4y²)+(-5x² + 3xy - y²) = 7x² − 2xy − 4y²-5x² + 3xy - y²
= (7-5)x² +(−2+3)xy +(−4-1)y²
= 2x² +xy − 5y²


(iv) Term to be subtracted = 6x³ − 7x² + 5x − 3
Changing the sign of each term of the expression gives -6x³ + 7x² - 5x + 3.
On adding:
(4 − 5x + 6x² − 8x³)+(-6x³ + 7x² - 5x + 3) = 4 − 5x + 6x² − 8x³-6x³ + 7x² - 5x + 3
= (-8-6)x³ +(6+7)x² +(-5- 5)x + 7
= -14x³ + 13x² - 10x + 7

(v) Term to be subtracted = x³ + 2x²y + 6xy² − y³
Changing the sign of each term of the expression gives -x³ - 2x²y - 6xy² + y³.
On adding:
(y³ − 3xy² − 4x²y)+(-x³ - 2x²y - 6xy² + y³) = y³ − 3xy² − 4x²y-x³ - 2x²y - 6xy² + y³
= -x³ +(- 2-4)x²y +(-6-3)xy² + (1+1)y³
= -x³ - 6x²y - 9xy² + 2y³

(vi) Term to be subtracted = −11x²y² + 7xy −6
Changing the sign of each term of the expression gives 11x²y² -7xy +6.
On adding:
(9x²y² −6xy + 9)+(11x²y² -7xy +6) = 9x²y² −6xy + 9+11x²y² -7xy +6
= (9+11)x²y² (-7−6)xy + 15
= 20x²y² −13xy +15

(vii) Term to be subtracted = −2a + b + 6d
Changing the sign of each term of the expression gives 2a-b-6d.
On adding:
(5a − 2b -3c)+(2a-b-6d ) = 5a − 2b -3c +2a-b-6d
= (5+2)a+(− 2-1)b -3c -6d
= 7a − 3b-3c -6d