Perfect Square of Quadratic Trinomials Rational Coefficients

Perfect Square of Quadratic Trinomials Rational Coefficients
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Now! again! x and x, what times what is one over nine? Well, I know that one over three times one over three is one over nine, and what about 1 over 3 plus 1 over 3? That’s 2 over 3, isn’t it, which is what we have in the middle, so I know that 1 over 3 and 1 over 3 is the right set of combinations. So I’m gonna put one over three there and one over three there. It’s both going to be positive because they’re all positive, okay? So I don’t have to worry about the negative signs.

Cross multiply, oh! I’ll first of all, rub this out. So we get a bit more room. Negative oh sorry 1 over 3 x that times that 1 over 3 x and if you add them together we know that 1 over 3 plus 1 over 3 is 2 over 3, so 2 over 3 x which is what we have in the middle. So always make sure, you check those. So it’s going to be x plus 1 over 3, x plus 1 over 3 which is x plus 1 over 3 squared, okay? So even if you get a fraction, even if you get a decimal you pretty much do the same thing, okay? But just leave it as a fraction form. That’s perfectly fine.

So question 19. Okay, we’ve got another fraction but again guys keep it the same way.

We know that a quarter is a half time a half and because we have a negative we must have negative half and negative half because negative negative makes the positive. Now, x and x on our left, negative half and negative half on our right cross multiply, we’ve got negative half x, cross multiply and then negative half minus a half is negative one so negative one x negative x which is same as that, so we’ve got the right set so we get x minus a half and x minus a half which is x minus a half squared, okay because it’s a perfect square.

This time we’ve got a decimal but as we did for fractions just keep it the same way. Just consider it as a decimal. So guys we’ve got 0.01. What squared is that? Well, it’s going to be 0.1 times 0.1, isn’t it? But we’ve got a positive here so we don’t have to worry about any signs. So I’m going to put my x and x and 0.1 0.1, okay? And cross multiply, cross multiply,
stick the x in the front and we know that 0.1 plus 0.1 is 0.2. So I’ve got 0.2 x and it must be the same as this. So we’ve got x plus that, x plus that, says x plus 0.1 squared, okay?

That’s exactly the same, just keep it in this decimal form because the question is in decimal form so trying to keep it the same form as the question, okay? And that’s pretty much it. That was some perfect squares.


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