Symplifying Algebraic Expressions: Problems with Solutions

Solution:
[tex]40 - 9x^{2} = 40 - 9(-3)^{2} = 40 - 9(9) = 40 - 81 = -41[/tex]

Solution:
[tex]x^{2} - 3xm - m + 4 = (2)^{2} - 3(2)(3) - 3 + 4 = 4 - 18 - 3 + 4 = -13[/tex]

Solution:
[tex]t^{4} - t^{3} - 4t + 18 = 2^{4} - 2^{3} - 4(2) + 18 = 16 - 8 - 8 + 18 = 18[/tex]

Solution:
[tex]9(x - 2y) = 9[3 - 2(-2)] = 9(3 + 4) = 9(7) = 63[/tex]

Solution:
[tex]x(x + 5) = x \times x + x \times 5 = x^{2} + 5x[/tex]

Solution:
$(x - 7)x = x\cdot x + (-7)\cdot x = x^2 - 7x$

Solution:
[tex]\frac{8x^2y}{4xy} = \frac{8}{4} \times \frac{x^2}{x} .\frac{y^2}{y} = 2x \times 1 = 2x [/tex]

Solution:
A minus sign in front of brackets changes the sign of every term inside:
[tex](4x^2-5x+2)-(2+3x-x^2)=4x^2-5x+2-2-3x+x^2=5x^2-8x[/tex]

Solution:
A minus sign in front of brackets changes the sign of every term inside:
[tex]A=5x^2-3x^2-2x+1+x^2+2x-5[/tex]
[tex]A=(5-3+1)x^2+(-2+2)x+(1-5)=3x^2-4[/tex]

Solution:
[tex]4x(x^2-x+2)-2x^2(2x-5)-8x+1=4x^3-4x^2+8x-4x^3+10x^2-8x+1[/tex]
[tex]=6x^2+1[/tex]

Solution:
We use the formula [tex](a-b)(a+b)=a^2-b^2[/tex]:
[tex](4x^2-9)-(x^2-9)=4x^2-9-x^2+9=3x^2[/tex]

Solution:
First we simplify:
[tex]A=9x^2+9x-5x-5-5x^2-10x=4x^2-6x-5[/tex]
[tex]x=-\frac{5}{2}[/tex]: [tex]A=4\times \frac{25}{4}-6\times \left(-\frac{5}{2}\right)-5=25+15-5=35[/tex]

Solution:
First we simplify:
[tex]2y(x-1)-2[xy-3(y+1)]=2xy-2y-2xy+6y+6=4y+6[/tex]
[tex]-x\{2y(x-1)-2[xy-3(y+1)]\}=-x(4y+6)[/tex]
[tex]y=-\frac{3}{2}[/tex]: [tex]4y+6=4\times \left(-\frac{3}{2}\right)+6=0[/tex]
Answer: [tex]0[/tex]

Solution:
Left-hand side: [tex](a-b)^2+(a-b)(a+b)=a^2-2ab+b^2+a^2-b^2=2a^2-2ab[/tex]
Right-hand side: [tex]2a(a-b)=2a^2-2ab[/tex]
Both sides are equal, so the identity is true.