Answer:
1) Solving the term [tex](3x + 5)(2x - 3)[/tex] using F.O.I.L we get [tex]\mathbf{6x^2+x-15}[/tex]
2) solving the term [tex](x + 2)(x - 13)[/tex] using F.O.I.L we get [tex]\mathbf{x^2-11x-26}[/tex]
3) Solving [tex](x+5)^2[/tex] using square of binomial we get [tex]\mathbf{x^2+10x+25}[/tex]
4) Solving [tex](x+5)^2[/tex] using square of binomial we get [tex]\mathbf{x^2-6x+9}[/tex]
Step-by-step explanation:
1) (3x + 5)(2x - 3). Solve using the F.O.I.L.
F.O.I.L stands for First, Outer Inner Last
We have [tex](3x + 5)(2x - 3)[/tex]
First: 3x(2x)
Outer: 3x(-3)
Inner: 5(2x)
Last: 5(-3)
Solving we get:
[tex](3x + 5)(2x - 3)\\=3x(2x)+3x(-3)+5(2x)+5(-3)\\=6x^2-9x+10x-15\\=6x^2+x-15[/tex]
So, solving the term [tex](3x + 5)(2x - 3)[/tex] using F.O.I.L we get [tex]\mathbf{6x^2+x-15}[/tex]
2) (x + 2)(x – 13). Solve using the F.O.I.L.
F.O.I.L stands for First, Outer Inner Last
We have [tex](x + 2)(x -13)[/tex]
First: x(x)
Outer: x(-13)
Inner: 2(x)
Last: 2(-13)
Solving we get:
[tex](x + 2)(x - 13)\\=x(x)+x(-13)+2(x)+2(-13)\\=x^2-13x+2x-26\\=x^2-11x-26[/tex]
So, solving the term [tex](x + 2)(x - 13)[/tex] using F.O.I.L we get [tex]\mathbf{x^2-11x-26}[/tex]
3) (x + 5)^2. Solve using the square of Binomial.
The square of binomial is: [tex](a+b)^2=a^2+2ab+b^2[/tex]
Solving:
[tex](x+5)^2\\=(x)^2+2(x)(5)+(5)^2\\=x^2+10x+25[/tex]
So, solving [tex](x+5)^2[/tex] using square of binomial we get [tex]\mathbf{x^2+10x+25}[/tex]
4) (x -3)^2. Solve using the square of Binomial.
The square of binomial used is: [tex](a-b)^2=a^2-2ab+b^2[/tex]
Solving:
[tex](x-3)^2\\=(x)^2-2(x)(3)+(3)^2\\=x^2-6x+9[/tex]
So, solving [tex](x+5)^2[/tex] using square of binomial we get [tex]\mathbf{x^2-6x+9}[/tex]
