For any value of x the value of the expression (x–3)(x+7)–(x+5)(x–1) is equal to –16.
Step-by-step explanation:
In order to prove the statement we can take any value of x and then solve the expression to see if it equal to -16 or not.
So,
Taking x = 2
[tex]=(x-3)(x+7)-(x+5)(x-1)\\=(2-3)(2+7)-(2+5)(2-1)\\=(-1)(9)-(7)(1)\\=-9-7=-16[/tex]
Taking x = 5
[tex]=(x-3)(x+7)-(x+5)(x-1)\\=(5-3)(5+7)-(5+5)(5-1)\\=(2)(12)-(10)(4)\\=24-40\\=-16[/tex]
Taking x= 10
[tex]=(x-3)(x+7)-(x+5)(x-1)\\=(10-3)(10+7)-(10+5)(10-1)\\=(7)(17)-(15)(9)\\=119-135=-16[/tex]
Hence,
For any value of x the value of the expression (x–3)(x+7)–(x+5)(x–1) is equal to –16.
Keywords: Polynomials, expressions
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