Option C
When [tex](2x - 3)^2[/tex] is subtracted from [tex]5x^2[/tex] then the result is [tex]x^2 + 12x - 9[/tex]
Solution:
Given that [tex](2x - 3)^2[/tex] is subtracted from [tex]5x^2[/tex]
We have to find the result
Subtraction is a mathematical operation that tells us the difference between two numbers.
When "a" is subtracted from "b", we write in mathematical expression as "b - a"
So [tex](2x - 3)^2[/tex] is subtracted from [tex]5x^2[/tex] is written mathematically as:
[tex]\rightarrow 5x^2 - (2x - 3)^2[/tex]
Expanding the above expression using algebraic identity:
[tex](a-b)^2 = a^2 - 2ab + b^2[/tex]
[tex]\rightarrow 5x^2 - ((2x)^2 -2(2x)(3) + (3)^2)\\\\\rightarrow 5x^2 - (4x^2 - 12x + 9)[/tex]
Multiplying the nnegative sign with terms inside bracket
There are two simple rules to remember:
- When you multiply a negative number by a positive number then the product is always negative.
- When you multiply two negative numbers or two positive numbers then the product is always positive.
[tex]\rightarrow 5x^2 - (4x^2 - 12x + 9)\\\\\rightarrow 5x^2 - 4x^2 + 12x -9\\\\\rightarrow x^2 + 12x - 9[/tex]
Hence the result is: [tex]x^2 + 12x - 9[/tex]
