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The product of (x - 9) and (x + 8) is:
x2+x+72
x2тИТxтИТ72
x2+72
x2+2xтИТ72
x2тИТxтИТ72
Use the sum-product rule: identify the sum of constants (-9 + 8 = -1) and the product (-9 * 8 = -72). The expression is x2+(sum)x+(product).
We are given two algebraic expressions: (x - 9) and (x + 8).
(x+a)(x+b)=x2+(a+b)x+ab
Use the sum-product rule: identify the sum of constants (-9 + 8 = -1) and the product (-9 * 8 = -72). The expression is x2+(sum)x+(product).
Students often miscalculate the sum of integers with different signs, leading to +x instead of тИТx, or ignore the negative sign in тИТ72.
Identify the constants
From the expression (xтИТ9)(x+8), compare with the identity (x+a)(x+b) where a=тИТ9 and b=8.
a=тИТ9,b=8
Calculate the coefficient of x
Find the sum of the constants (a+b) to determine the linear term coefficient.
(тИТ9+8)=тИТ1
Calculate the constant term
Find the product of the constants (a├Чb) to determine the constant term.
(тИТ9)├Ч(8)=тИТ72
Construct the final expression
Combine the terms into the standard quadratic form x2+(sum)x+(product).
x2тИТxтИТ72
B is correct because the expansion of (xтИТ9)(x+8) results in x2тИТxтИТ72 after summing the coefficients.
This identity is fundamental for solving quadratic equations by factoring; mastering this allows for faster root-finding in higher-level algebra.
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