Answer:
[tex](2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14[/tex]
Step-by-step explanation:
To explain how to approach this question, I am going to place letters in the blank spaces:
[tex](ax^2+bx+c)-(dx^2+ex+f)=-5x^2-14[/tex]
First, compare the coefficients of the x² terms on both sides of the equation: [tex]a - d = -5[/tex]
Therefore, we need to choose any two numbers in place of a and d whose difference is -5:
⇒ a = 2 and d = 7 as 2 - 7 = -5.
Similarly, upon comparing the coefficients of the x terms, we can see that there is no x term on the right side of the equation. Therefore, we need to choose numbers in place of b and e for which the difference is zero. So b and e should be the same number:
⇒ b = 2 and e = 2 as 2 - 2 = 0.
Finally, compare the constant term on both sides of the equation: [tex]c - f = -14[/tex]
Therefore, we need to choose any two numbers in place of c and f whose difference is -14:
⇒ c = 1 and f = 15 as 1 - 15 = -14.
Plug in the numbers in place of the letters on the left side of the equation:
[tex](2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14[/tex]
Check
Remove the brackets:
[tex]2x^2+2x+1-7x^2-2x-15=-5x^2-14[/tex]
Collect like terms:
[tex]2x^2-7x^2+2x-2x+1-15=-5x^2-14[/tex]
Combine like terms:
[tex]-5x^2-14=-5x^2-14[/tex]
Hence proving that the left and right sides of the equation are the same.
