1. (x + 3) square + (x + 2) (X-2) 2. Solve the binary linear equation: {5x-2y = 4 {2x-3y = - 5

1. (x + 3) square + (x + 2) (X-2) 2. Solve the binary linear equation: {5x-2y = 4 {2x-3y = - 5

1. (x + 3) square + (x + 2) (X-2)
=x²+6x+9+x²-4
=2x²+6x+5
2
{ 5x-2y=4 ①
{2x-3y=-5 ②
① X 3 - 2 × 2 was obtained
15x-4x=12+10
11x=22
∴x=2
Y=3
4x2-45 = 31 factorized
Original formula:
4x^2-76=0
4(x^2-19)=0
x^2-19=0
(x+√19)(x-√19)=0
x=±√19
X plus (56 minus 44 minus 1 in 4) divided by 1 in 5 equals 56,
x+(56-44-x/4)/1/5=56
x+280-220-5x/4=56
4x+240-5x=224
-x=-16
x=16
4x2-12x + 9 =? Factorization
Analysis: direct use of complete square formula can be decomposed
4x²-12x+9
=(2x-3)²
（2x-3）²
(2x-3)²
The solution of the equation is 7556 percent
32+0.75x=56
0.75x=24
x=32
Factorization of 4x2-9y2
4x²-9y²
=(2x)²-(3y)²=(2x+3y)(2x-3y)
Hello
Original formula = (2x-3y) (2x + 3Y)
Principle: A ^ 2-B ^ 2 = (a + b) (a-b) can be used flexibly
（2X+3Y）（2X-3Y）
Solving equation 1 / 8y + 12 = 1 / 20 + 36
It's 1 / 20Y + 36
1/8y+12=1/20y+36
1/8y-1/20y=36-12
5/40y-2/40y=24
3/40y=24
y=24x40/3
y=320
Factorization (1) 121 (a-b) & #178; - 169 (a + b) & #178; (2) a (n-1) & #178; - 2A (n-1) + A
(1)121(a-b)²-169(a+b)²=[11(a-b)]²-[13(a+b)²]=[11(a-b)+13(a+b)][11(a-b)-13(a+b)]=(24a+2b)(-2a-24b)=-4(12a+b)(a+12b)(2)a(n-1)²-2a(n-1)+a=a[(n-1)²-2(n-1)+1]=a[(n-1)-1]²...
(1) 121（a-b)²-169(a+b)²
=[11(a-b)]²-[13(a+b)]²
=[11(a-b)+13(a+b)][11(a-b)-13(a+b)]
=(11a-11b+13a+13b)(11a-11b-13a-13b)
=(24a+2b)(-2a-24b)
=-4(12a+b)(a+12b)
(2) a(n-1)²-2a(n-1)+a
=a[(n-1)²-2(n-1)+1]
=a(n-1-1)²
=a(n-2)²
(1) 121（a-b)²-169(a+b)²
=[11（a-b)]²-[13(a+b)]²
=[11（a-b)+13(a+b)][11（a-b)-13(a+b)]
=(11a-11b+13a+13b)(11a-11b-13a-13b)
=(24a+2b)(-2a-24b)
=-4(12a+b)(a+12b)
(2) a(n-1)²-2a(n-1)+a
=a[(n-1)²-2(n-1)+1]
=a(n-1-1)²
=a(n-2)²
① Solution {11 (a-b) - 13 (a + b)} {11 (a-b) + 13 (a + b)}
=-4（a+12b）（12a+b）
② Solution a (n-1) ^ 2-2a (n-1) + A
=a{（n-1）^2-2（n-1）+1}
=a{（n-1）-1}^2
=a（n-2）^2
Solution: (1) the original formula = [11 (a-b)] square - [13 (a + b)] square = (11a-11b + 13A + 13b) (11a-11b-13a-13b) = (24a + 2b) (- 2a-24b) = - 2 (12a + b) square. (2) The original formula = a [(n-1) square-2 (n-1) + 1] = a (n-1-1) square = a (A-2) square.
Read the following materials: when doing the practice of solving equations, there is an equation "2y-12 = 18y + ■" in the study paper. Xiao Cong asked the teacher, but the teacher just said: "it is a rational number, and the solution of the equation is the same as the value of the algebraic formula 5 (x-1) - 2 (X-2) - 4 when x = 3." smart Xiao Cong quickly added this constant. Students, please also add this constant Constant
Substituting x = 3 into 5 (x-1) - 2 (X-2) - 4, 5 (x-1) - 2 (X-2) - 4 = 3x-5 = 4, substituting y = 4 into the original equation, 8-12 = 12 + ■, the solution is: ■ = 7
Let's decompose the following formulas into factors 0.25q & # 178; - 121p & # 178; =? 169x & # 178; - 4Y & # 178; =?
=(0.5q)^2-(11p)^2=(0.5q+11p)*(0.5q-11p)
=(13x)^2-(2y)^2=(13x+2y)*(13x-2y)