Selina solutions

Question 9

Q10) Subtract:

(i) 4x from 8 - x

(ii) -8c from c + 3d

(iii) -5a - 2b from b + 6c

(iv) 4p+p^2\ from\ 3p^2-8p

(v) 5a - 3b + 2c from 4a - b - c

(vi) - xy + yz - zx from xy - yz + xz

(vii) 2x^2-7xy-y^2\ from\ 3x^3-5xy+3y^2

(viii) a^2-3ab-6b^2\ from\ 2b^2-a^2+2ab

(ix) 4x^2-5x^2y+y^2\ from\ 3y^2+5xy^2-7x^2-9x^2y

(x) 6m^3+4m^2+7m-3\ from\ 3m^3+4

Solution 10:

(i) 4x from 8 - x

= 8 - x - 4x

= 8 - 5x

(ii) -8c from c + 3d

= c + 3d - (-8c)

= c + 3d + 8c

= 9c + 3d

(iii) -5a - 2b from b + 6c

= b + 6c - (-5a - 2b)

= b + 6c + 5a + 2b

= 5a + 3b + 6c

(iv) 4p+p^2\ from\ 3p^2-8p

= 3p^2-8p-\left(4p+p^2\right)

= 3p^2-8p-4p-p^2

= 2p^2-12p

(v) 5a - 3b + 2c from 4a - b - c

= 4a - b - c - (5a - 3b + 2c)

= 4a - b - c - 5a + 3b - 2c

= -a + 2b - 3c

(vi) - xy + yz - zx from xy - yz + xz

= xy - yz - xz - (-xy + yz - zx)

= xy - yz + xz + xy - yz + xz

= 2xy - 2yz + 2xz

(vii) 2x^2-7xy-y^2\ from\ 3x^3-5xy+3y^2

= 3x^2-5xy+3y^2-\left(2x^2-7xy-y^2\right)

= 3x^2-5xy+3y^2-2x^2+7xy+y^2

= x^2+2xy+4y^2

(viii) a^2-3ab-6b^2\ from\ 2b^2-a^2+2ab

= 2b^2-a^2+2ab-\left(a^2-3ab-6b^2\right)

= 2b^2-a^2+2ab-a^2+3ab+6b^2

= -2a^2+5ab+8b^2

(ix) 4x^2-5x^2y+y^2\ from\ 3y^2+5xy^2-7x^2-9x^2y

= -3y^2+5xy^2-7x^2-9x^2y\ -\left(4x^2-5x^2y+y^2\right)

= -3y^2+5xy^2-7x^2-9x^2y-4x^2+5x^2y-y^2

= -4x^2y-4y^2+5xy^2-11x^2

(x) 6m^3+4m^2+7m-3\ from\ 3m^3+4

= 3m^3+4-\left(6m^3+4m^2+7m-3\right)

= 3m^3+4-6m^3-4m^2-7m+3

= -3m^3-4m^2-7m\ +7

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