Answer:
Step-by-step explanation:
The terms will be multiplied in order to get the simplified polynomials.
a. 6(x + 7)(x + 2)
[tex]6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84[/tex]
The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. (2y – 5)^2
Using the formula: [tex](a-b)^2 = a^2+b^2-2ab[/tex]
[tex]=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y[/tex]
The simplified form is: [tex]4y^2-20y+25[/tex]
c. (5x + 4y)(2x - y)
[tex]=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2[/tex]
The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. (3x + 7)(3x – 7)
Using the formula: [tex](a+b)(a-b) = a^2-b^2[/tex]
[tex]= (3x)^2-(7)^2\\= 9x^2-49[/tex]
The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. (t + 2) – (4t +9) – t
[tex]=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7[/tex]
The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
Hence,
a. The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]
b. The simplified form is: [tex]4y^2-20y+25[/tex]
c. The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]
d. The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]
e. The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]
