Alright I'm doing a maths review (grade 11) and on the page, the subtitle says "Quadratics" and then underneath is the questions, no instructions. I figured out the first one "y^2+2y+1" and got to "(y+1)^2", but the second question is "49-(2y-w)^2".
I can't figure out what to do with it... should I expand it out and deal with it or will I get right back to that? I think maybe it's confusing me because it's in a different format, but I'd like some help, thanks.
The second is a difference of two squares.
7^2-u^2 where u=2y-w
Thank you so much for clarifying, I think it was a little foggy in my mind because it looked different from the others, but now that you say difference of squares, it makes total sense... I'll have to keep that in mind for the test!
It's great that you've already figured out the first question! For the second question, "49-(2y-w)^2," you can indeed begin by expanding it out to simplify the expression.
To expand the expression, you can use the formula for expanding a binomial square, which is (a - b)^2 = a^2 - 2ab + b^2. In this case, the binomial is (2y - w), so we have:
49 - (2y - w)^2 = 49 - [(2y)^2 - 2(2y)(w) + (w)^2]
Now, let's simplify further:
= 49 - (4y^2 - 4yw + w^2)
= 49 - 4y^2 + 4yw - w^2
And finally, combine like terms:
= -4y^2 + 4yw - w^2 + 49
So the simplified expression is -4y^2 + 4yw - w^2 + 49.
Remember, when dealing with quadratics, it's important to look for patterns or opportunities to factor or simplify the expression. In this case, expanding it out was the necessary step to simplify the expression.