Question

hi, could someone pls help me with the yellow highlight equation i tried asking my teacher for help and he explained but i still didnt understand. I understand the rest but not the yellow highlighted ones. Thank u!

Answer 1

Explanation:

Q5.

Given the 1st (U₁) pattern is 3, then adding 2 (d) to each subsequent pattern.

`\boxed{U_n=U_1+(n-1)d}`

Therefore, the general rule is:

`U_n=3+(n-1)(2)`

`=3+2n-2`

`=1+2n`

For 40th term → n = 40

`U_(40)=1+2(40)`

`=81`

Q6.

Factorise the numerator by grouping the common factors just like finding the GCF

16x⁴y⁶ = 2⁴x⁴y⁶

12x³y⁴ = 2²(3)x³y⁴

4x²y = 2²x²y

the GCF of the 3 terms = 2²x²y = 4x²y

16x⁴y⁶ = (4x²y)(4x²y⁵)

12x³y⁴ = (4x²y)(3xy³)

4x²y = (4x²y)(1)

`(16x^4y^6+12x^3y^4-4x^2y)/(4x^2y)`

`=((4x^2y)(4x^2y^5+3xy^3-1))/(4x^2y)`

`=4x^2y^5+3xy^3-1`