Secondary home school 12th grade
I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.
- (7x2 – 3yz)2 – (7x2 + 3yz)2
- Use Pascal’s triangle to expand (2x – y)4
- 8x3 y - x3 y4
- (m + 3n)2 – 144
- 12x4 y – 16x3 y2 – 60x2 y3
- p3 q2 – 9p3 + 27q2 – 243
A significant part of algebra is "pattern recognition". By that I mean the ability to look at an expression and see some underlying pattern. For example in problem 1 what I see is
which is a difference of squares and factors as
In other words,
a2 - b2 = (a - b)(a + b)
(7x2 – 3yz)2 – (7x2 + 3yz)2 = [(7x2 – 3yz) – (7x2 + 3yz)][(7x2 – 3yz) + (7x2 + 3yz)]
For probmem 3 there is an x and a y in each of the two terms. Hence x3y is a common factor and you can write
8x3 y - x3 y4 = x3y(8 - y3)
Since 8 = 23 this becomes
8x3 y - x3 y4 = x3y(23 - y3)
The pattern to recognize this time is that 23 - y3 is a difference of cubes that you can factor.
Now try problems 4, 5 and 6. You need to look for common factors and "patterns".
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