3 Tutor System
Starting just at 265/hour

# 4.(a) Subtract $$4a – 7ab + 3b + 12$$ from $$12a – 9ab + 5b – 3$$ (b) Subtract $$3xy + 5yz – 7zx$$ from $$5xy – 2yz – 2zx + 10xyz$$ (c) Subtract $$4p^2q – 3pq + 5pq^2 – 8p + 7q – 10$$ from $$18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q$$

(a)We have the expressions to subtract:$$4a – 7ab + 3b + 12$$ from $$12a – 9ab + 5b – 3$$
Subtracting these we get: $$(12a – 9ab + 5b – 3)-(4a – 7ab + 3b + 12 )$$

$$(12a – 9ab + 5b – 3)+(-4a +7ab - 3b - 12 )\quad$$[Taking (-) inside the second bracket]

$$\Rightarrow (12a-4a)+ (– 9ab+7ab)+ (+ 5b- 3b )+( – 3 - 12 )\quad$$[Placing like terms together]

$$\Rightarrow (8a)+ (-2ab)+ (2b)+(-15)$$

$$\Rightarrow (8a-2ab+ 2b-15)$$

(b)We have the expressions to subtract:$$3xy + 5yz – 7zx$$ from $$5xy – 2yz – 2zx + 10xyz$$
Subtracting these we get: $$(5xy – 2yz – 2zx + 10xyz)-(3xy + 5yz – 7zx)$$

$$(5xy – 2yz – 2zx + 10xyz)+(-3xy - 5yz + 7zx )\quad$$[Taking (-) inside the second bracket]

$$\Rightarrow (5xy-3xy )+ (– 2yz - 5yz)+ (– 2zx+ 7zx )+( + 10xyz )\quad$$[Placing like terms together]

$$\Rightarrow (2xy)+ (-7yz)+ (5zx)+(10xyz)$$

$$\Rightarrow (2xy-7yz+5zx+10xyz)$$

(c)We have the expressions to subtract:$$4p^2q – 3pq + 5pq^2 – 8p + 7q – 10$$ from $$18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q$$
Subtracting these we get: $$(18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q )-(4p^2q – 3pq + 5pq^2 – 8p + 7q – 10)$$

$$\Rightarrow(18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q)+(-4p^2q +3pq-5pq^2 +8p-7q+ 10)\quad$$[Taking (-) inside the second bracket]

$$\Rightarrow (+18+10)+(-3p+8p)+(-11q-7q)+(5pq+3pq)+(-2pq^2-5pq^2)+(+ 5p^2q-4p^2q) \quad$$[Placing like terms together]

$$\Rightarrow (+28)+ (+5p)+(-18q)+(8pq)+(-7pq^2)+(+p^2q)$$

$$\Rightarrow (+28+5p-18q+8pq-7pq^2+p^2q)$$