Question

Subtract −5x^2+7x+2 from −5x^2−7x+2

Answer 1

-14x

Explanation:

-5x^2 -7x + 2 - (-5x + 7x + 2)

-5x^2 - 7x + 2 + 5x - 7x -2

-14x

Explanatory Step 0:

• When we want to subtract A from B, we're taking away from B so the equation is B - A

Step 1:

• Thus, the first expression (-5x^2 + 7x + 2) comes second and goes on the right side of the minus side,
• while the second expression (-5x^2 - 7x + 2) comes first and goes on the left side
• We'll need parentheses around the first expression (-5x^2 + 7x + 2) to do step 2

`-5x^2-7x+2-(-5x^2+7x+2)`

Step 2: We're subtracting the entire expression, so we can distribute the minus sign to everything in the parentheses and simplify by combining like terms:

`-5x^2-7x+2-(-5x^2+7x+2)\\-5x^2-7x+2+5x^2-7x-2\\(-5x^2+5x^2)+(-7x-7x)+(2-2)\\-14x`

Optional Step 3:

Since the simplified expression is -14x, we can check by plugging in a number for x and see that we get the same answer for the simplified expression, 14x, and the original subtraction expression, -5x^2 -7x + 2 - (-5x^2 + 7x + 2). Let's try 2 for x:

Plugging in 2 for x in simplified expression, -14x:

`-14(2)\\-28`

Plugging in 2 for x in original subtraction expression, -5x^2 -7x + 2 - (-5x^2 + 7x + 2):

`-5(2)^2-7(2)+2-(-5(2)^2+7(2)+2)\\-5*4-14+2-(-5*4+14+2)\\-20-12-(-20+16)\\-32-(-4)\\-32+4\\-28`

Since the two answers are the same, we've correctly subtracted -5x^2 + 7x + 2 from -5x^2 - 7x +2