Question

3. The factors of x²y² + xy² are

a. xy(x+y)
b. xy²(x +1)
c. x²y(x+y)
d. Xy(x+1)


4. The factors of x²-6x+8 are

a. (x+2)(x+4)
b. (x+2)(x-4)
c. ( x-2)(x-4)
d. ( x-2)(x+4)


5. The factors of x³-8 are

a. (x-2)(x²+2x+4)
b. (x-2)(x²–2x+4)
c. (x+2)(x²+2x+4)
d. (x+2)(x²–2x+4)​

Answer 1

Answer:

Try to separate it into different parts and try to use a substitution as follows:

step 1 factorise [math]x^2-y^2[/math] :

[math]x^2-y^2=(x+y)(x-y)[/math]

step 2 let [math]a=x-y[/math] :

so

[math]x^2-y^2+x-y=(x+y)(x-y)+(x-y)[/math]

replacing x-y to [math]a [/math]becomes

[math]x^2-y^2+x-y=(x+y)a+a[/math]

[math] =a((x+y)+1))[/math]

taking back from a the x-y:

[math]a((x+y)+1))=(x-y)(x+y+1)[/math]