Problem 1: Subtract $3a$ from $9a$.
Problem 2: Subtract $-5x$ from $4x$.
Problem 3: Subtract $7y$ from $-2y$.
Problem 4: Subtract $4x – 5y$ from $6x + 3y$.
Problem 5: Subtract $-3a + 2b$ from $5a – 4b$.
Problem 6: If $A = x^2 + 3x + 4$ and $B = 2x^2 – x + 1$, find $(i) A – B$.
Problem 7: If $P = 3x^2 – 2x + 5$ and $Q = x^2 + 4x – 7$, find $(i) P – Q$.
Problem 8: Using vertical method, subtract $2x + 3y$ from $5x – y$.
Problem 9: Using vertical method, subtract $a^2 – b^2 + ab$ from $2a^2 + 3b^2 – ab$.
Problem 10: Using vertical method, subtract $4m – 2n + 3$ from $7m + n – 5$.
1. Subtract $3a$ from $9a$.
Setup: $9a – 3a$
Explanation: Since both terms are “like terms” (they both have $a$), simply subtract the coefficients: $9 – 3 = 6$.
Answer: $6a$
2. Subtract $-5x$ from $4x$.
Setup: $4x – (-5x)$
Explanation: Subtracting a negative is the same as adding a positive. This becomes $4x + 5x$.
Answer: $9x$
3. Subtract $7y$ from $-2y$.
Setup: $-2y – 7y$
Explanation: You are starting at $-2$ and moving $7$ more units in the negative direction. Think of it as $-2 + (-7)$.
Answer: $-9y$
4. Subtract $4x – 5y$ from $6x + 3y$.
Setup: $(6x + 3y) – (4x – 5y)$
Explanation: Distribute the negative sign: $6x + 3y – 4x + 5y$. Group like terms: $(6x – 4x) + (3y + 5y)$.
Answer: $2x + 8y$
5. Subtract $-3a + 2b$ from $5a – 4b$.
Setup: $(5a – 4b) – (-3a + 2b)$
Explanation: Distribute the negative: $5a – 4b + 3a – 2b$. Combine $a$ terms ($5 + 3$) and $b$ terms ($-4 – 2$).
Answer: $8a – 6b$
6. If $A = x^2 + 3x + 4$ and $B = 2x^2 – x + 1$, find $A – B$.
Setup: $(x^2 + 3x + 4) – (2x^2 – x + 1)$
Explanation: Flip all signs in expression $B$: $x^2 + 3x + 4 – 2x^2 + x – 1$. Combine like terms: $(1-2)x^2 + (3+1)x + (4-1)$.
Answer: $-x^2 + 4x + 3$
7. If $P = 3x^2 – 2x + 5$ and $Q = x^2 + 4x – 7$, find $P – Q$.
Setup: $(3x^2 – 2x + 5) – (x^2 + 4x – 7)$
Explanation: Flip the signs of $Q$: $3x^2 – 2x + 5 – x^2 – 4x + 7$. Combine like terms: $(3-1)x^2 + (-2-4)x + (5+7)$.
Answer: $2x^2 – 6x + 12$
For these, align the terms vertically and change the signs of the bottom row.
8. Subtract $2x + 3y$ from $5x – y$.
Explanation: Write $5x – y$ on top. Below it, write $-2x – 3y$ (signs changed). Add vertically.
Answer: $3x – 4y$
9. Subtract $a^2 – b^2 + ab$ from $2a^2 + 3b^2 – ab$.
Explanation: Align terms: $(2a^2 – a^2) + (3b^2 + b^2) + (-ab – ab)$. Remember that $-(-b^2)$ becomes $+b^2$.
Answer: $a^2 + 4b^2 – 2ab$
10. Subtract $4m – 2n + 3$ from $7m + n – 5$.
Explanation: Align and flip bottom signs: $7m + n – 5$ on top, and $-4m + 2n – 3$ on bottom.
Answer: $3m + 3n – 8$