(2a-5) ^ 2, calculated by the square difference formula

(2a-5) ^ 2, calculated by the square difference formula

(2a-5)^2
=(2a)²-2x5x2a+5²
=4a²-20a+25
If you don't understand this question, you can ask,

1. Given a = 3x square - 6xy + y square, B = - x square - 5xy - 7Y square, find A-B and - 3A + 2B
fast

A-B = 4x-xy + y + 7Y
-3A + 2B = - 11x + 8xy-3y-14y

A real symmetric matrix of order n is positive semidefinite if and only if a + ki is positive definite for any K

Because a is positive semidefinite
So for any nonzero n-dimensional vector x, x'ax > = 0
And X '(KI) x = KX'x
So if a + ki is positive definite, there must be x '(a + Ki) x > 0
That is KX'x > 0
So k > 0
Your topic is wrong

How to do 2x (x-3) = (x-3) factorization

2x(x-3)=(x-3)
2x(x-3)-(x-3)=0
(x-3)(2x-1)=0
X-3 = 0 or 2x-1 = 0
The solution is x = 3 or x = 1 / 2

2a-24 (3a-b-k) = 0, then what is the value of K when B is negative

2a-24 (3a-b-k)=0,
b=(24k-70a)/24

Let a be a constant, f (x) = x & sup2; - 4x + 3, if f (x + a) is an even function, find a
RT

f(x+a)
=(x+a)²-4(x+a)+3
=x²+2ax+a²-4x-4a+3
=x²+(2a-4)x+(a²-4a+3)
Because the function is even,
So when x is converted to - x, the results are equal
Then the coefficient with odd power of X must be 0
So 2a-4 = 0
a=2

Point a (2,1) is on the image with inverse scale function y = K / x, when 1

First, we substitute a (2,1) into y = K / X
So K / 2 = 1, so k = 2
So y = 2 / X
Then substitute x = 1, x = 4 into y = 2 / X
When x = 1, y = 2, and x = 4, y = 0.5
So the value range of Y is greater than 0.5 and less than 2

When several rational numbers are multiplied, when the number of negative factors is odd, the product must be negative
When the product is negative, the number of negative factors is odd
Are these two sentences right

It's not appropriate to use the word negative factor here. It's better to use negative number instead
When several rational numbers are multiplied, when the number of negative numbers is odd, the product must be negative
Error. It's possible that the multiplier has 0
When the product is negative, there are odd negative numbers in the multiplier
correct

The calculation problem (- 4x-3y Square) (3Y square-4x) is fast,

(- 4x-3y squared) (3Y squared-4x)
=(4x+3y²)(4x-3y²)
=The fourth power of 16x & # 178; - 9y

Several solutions of X-cube + 6x & sup2; + 11x + 6

(1) X = - 1, the original polynomial is 0. X + 1 is a factor
Original formula = (x + 1) (x ^ 2 + ax + 6)
From the undetermined coefficient method, a = 5 can be obtained
Original formula = (x + 1) (x ^ 2 + 5x + 6) = (x + 1) (x + 2) (x + 3)
(2) Original formula = (x ^ 3 + 6x ^ 2 + 9x) + 2 (x + 3)
=x(x+3)^2+2(x+3)
=(x^2+3x+2)(x+3)=(x+1)(x+2)(x+3)
(3) Original formula = x ^ 3 + x ^ 2 + 5x ^ 2 + 5x + 6x + 6
=x(x+1)+5x(x+1)+6(x+1)
=(x^2+5x+6)(x+1)=(x+2)(x+3)(x+1)
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