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2 Responses
You’re expanding it correctly; the only step left is to combine like terms. Distribute 2x across (x − 5) to get 2x·x = 2x^2 and 2x·(−5) = −10x, then distribute +3 across (x − 5) to get 3·x = 3x and 3·(−5) = −15. Putting these together gives 2x^2 − 10x + 3x − 15, and combining the x-terms yields 2x^2 − 7x − 15. Quick sign check: the x^2 term is positive (positive times positive) and the constant is negative (positive times negative), which matches. Want to try one more, maybe with both binomials having negatives, to reinforce the sign handling?
You’re right on track with the “handing out coupons” idea! Distribute each term in the first bracket to both terms in the second. So (2x+3)(x−5) becomes 2x·x = 2x^2, 2x·(−5) = −10x, 3·x = 3x, and 3·(−5) = −15. Put those together: 2x^2 −10x + 3x −15, and then combine the like terms in the middle to get 2x^2 − 7x − 15. The only place people usually stumble is the signs-just remember the little multiplication rules: plus×minus = minus, minus×minus = plus.
Quick extra example to lock it in: (x−4)(x−2). Multiply across: x·x = x^2, x·(−2) = −2x, (−4)·x = −4x, and (−4)·(−2) = +8. Add them up: x^2 − 2x − 4x + 8 = x^2 − 6x + 8. Same “coupon” idea, and notice how the last term turned positive because a negative times a negative is a positive. You’ve got it!