a
2 – 2ab + b2 = ________________
Answers
Answer:
it's his a formula of (a+b) the whole square
Answer:
1 In general, given a{x}^{2}+bx+cax
2
+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 In this case, a=1a=1, b=-2ab=−2a and c=2c=2.
(b-\frac{2a+\sqrt{{(-2a)}^{2}-4\times 2}}{2})(b-\frac{2a-\sqrt{{(-2a)}^{2}-4\times 2}}{2})
(b−
2
2a+
(−2a)
2
−4×2
)(b−
2
2a−
(−2a)
2
−4×2
)
3 Simplify.
(b-\frac{2a+2\sqrt{{a}^{2}-2}}{2})(b-\frac{2a-2\sqrt{{a}^{2}-2}}{2})
(b−
2
2a+2
a
2
−2
)(b−
2
2a−2
a
2
−2
)
4 Factor out the common term 22.
(b-\frac{2(a+\sqrt{{a}^{2}-2})}{2})(b-\frac{2a-2\sqrt{{a}^{2}-2}}{2})
(b−
2
2(a+
a
2
−2
)
)(b−
2
2a−2
a
2
−2
)
5 Cancel 22.
(b-(a+\sqrt{{a}^{2}-2}))(b-\frac{2a-2\sqrt{{a}^{2}-2}}{2})
(b−(a+
a
2
−2
))(b−
2
2a−2
a
2
−2
)
6 Remove parentheses.
(b-a-\sqrt{{a}^{2}-2})(b-\frac{2a-2\sqrt{{a}^{2}-2}}{2})
(b−a−
a
2
−2
)(b−
2
2a−2
a
2
−2
)
7 Factor out the common term 22.
(b-a-\sqrt{{a}^{2}-2})(b-\frac{2(a-\sqrt{{a}^{2}-2})}{2})
(b−a−
a
2
−2
)(b−
2
2(a−
a
2
−2
)
)
8 Cancel 22.
(b-a-\sqrt{{a}^{2}-2})(b-(a-\sqrt{{a}^{2}-2}))
(b−a−
a
2
−2
)(b−(a−
a
2
−2
))
9 Remove parentheses.
(b-a-\sqrt{{a}^{2}-2})(b-a+\sqrt{{a}^{2}-2})
(b−a−
a
2
−2
)(b−a+
a
2
−2
)
Done