Unit 7 · Topic 02 · Algebraic Expressions
Kabir subtracted (3x − 2y) from (5x + 4y) and forgot to flip a single sign.
His answer was off by exactly 4y — the whole subtracted bracket had two terms, and he only flipped one.
One missed sign, and the entire second half of the expression came out wrong.
Ms. Rao wrote: subtract (2a + 3b) from (7a + 5b). Kabir set it up: (7a + 5b) − (2a + 3b).
"Now distribute that minus sign," said Ms. Rao. "It applies to EVERY term inside the bracket, not just the first one."
Kabir wrote: 7a + 5b − 2a − 3b, carefully flipping both +2a to −2a AND +3b to −3b.
"Now group like terms." (7a − 2a) + (5b − 3b) = 5a + 2b.
"Correct," said Ms. Rao. She then wrote a trickier one: subtract (3x − 2y) from (5x + 4y).
Kabir set it up: (5x + 4y) − (3x − 2y). "The bracket has a minus sign INSIDE it already. What happens when I distribute the outer minus?"
"Every sign inside flips," said Ms. Rao. "+3x becomes −3x. And −2y — already negative — becomes +2y when the outer minus flips it again."
Kabir wrote it carefully: 5x + 4y − 3x + 2y. He grouped: (5x − 3x) + (4y + 2y) = 2x + 6y.
"That's exactly where students usually lose a sign," said Ms. Rao. "A minus outside a bracket containing a minus inside flips into a plus — two negatives combining into a positive, same rule as integer subtraction."
Anaya tried it a different way, to double check. She computed 5x + 4y and 3x − 2y as if x=10, y=1: first is 54, second is 28. 54 − 28 = 26. Then she checked 2x + 6y with the same values: 20 + 6 = 26. "Matches. The algebra rule really does work."
"Substituting numbers to check your algebra is a genuinely useful habit," said Ms. Rao. "If the numbers don't match, you know a sign got lost somewhere in the brackets."
Subtracting one expression from another means distributing the minus sign across EVERY term inside the subtracted bracket, not just the first one.
A plus sign inside a subtracted bracket becomes a minus: (A) − (+B) = A − B.
A minus sign inside a subtracted bracket becomes a plus: (A) − (−B) = A + B — same rule as subtracting a negative integer.
After distributing the minus sign across the whole bracket, group like terms exactly as in addition, and simplify.
Subtract (3m − 2n) from (8m + 5n), showing every sign flip.
Check your answer by substituting m=5, n=2 into both the original and simplified expressions.
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