Every term of one meets every term of the other
Two brackets sit side by side: (x + 3)(x + 5). Neither bracket has a value until x is known.
x, 3; columns x, 5. Step 1 of 4
- Grid: rows
x,3; columnsx,5. xbyx→x².xby5and3byx→5xand3x.3by5→15. Total:x² + 8x + 15.
Rule: every term of one bracket meets every term of the other. Then join the like terms.
This works because (x + 3)(x + 5) is x(x + 5) + 3(x + 5).
At x = 2 the brackets give 5 × 7 = 35. And x² + 8x + 15 is 4 + 16 + 15 = 35.
A minus inside works the same way. The four pairings are x², −2x, 3x and −6. Then −2x + 3x = x, so (x + 3)(x − 2) = x² + x − 6.
Watch out!
The mistake pairs first with first: x by x. It pairs last with last: 3 by 5. That gives x² + 15. This answer matches at x = 0, by chance. At x = 5 it gives 25 + 15 = 40. The brackets give 8 × 10 = 80.
Slide x. Find where the short answer breaks.
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