Question

1. m(4 + p) + p(3+ m)

2. 4r(3 + 4p) + 3p(8 -r)
3. (3 + 2h)(5 + 3h)
4. (3 + 4y)(5y - 1)
5. (2n - 3p)(3p - 2m)

Expand and simplify each of the following . Please give me the correct answer. Thanks

Answer 1

Solutions :

`\sf1. \quad\: m(4 + p) + p(3+ m)`

`\sf \dashrightarrow \quad\: 4m + mp + 3p+ mp`

`\sf \dashrightarrow \quad\: 4m + 2mp + 3p`

⠀

`\sf 2. \quad\: 4r(3 + 4p) + 3p(8 -r)`

`\sf \dashrightarrow \quad\: 12r+ 16rp + 24p -3pr`

`\sf \dashrightarrow \quad\: 12r+ 13rp + 24p`

⠀

`\sf 3. \quad\: (3 + 2h)(5 + 3h)`

`\sf \dashrightarrow \quad\: 3(5 + 3h) + 2h(5 + 3h)`

`\sf \dashrightarrow \quad\: 15 + 9h + 10h + {6h}^(2)`

`\sf \dashrightarrow \quad\: 15 + 19h + {6h}^(2)`

⠀

`4. \sf \quad\:(3 + 4y)(5y - 1)`

`\sf \dashrightarrow \quad\:  3(5y - 1) + 4y(5y - 1)`

`\sf \dashrightarrow \quad\: 15y - 3 + 20y^2 - 4y`

`\sf \dashrightarrow \quad\: 11y - 3 + {20}^(2)`

⠀

`5.\sf \quad\: (2n - 3p)(3p - 2m)`

`\sf \dashrightarrow \quad\:  2n(3p - 2m) +[-3p(3p - 2m)]`

`\sf \dashrightarrow \quad\: 6np - 4mn -9p^2 + 6mp`

`\sf \dashrightarrow \quad\: -9p^2 - 4mn + 6mp + 6np`

Answer 2

1. 4m + 2mp + 3p

2. 12r + 13pr + 24p

3. 6h^2 + 19h + 15

4. 20y^2 + 11y - 3

5. -9p^2 - 4mn + 6mp + 6np

Explanation:

1. m(4 + p) + p(3+ m)

4m + mp + 3p + mp

4m + (mp + mp) + 3p

4m + 2mp + 3p

2. 4r(3 + 4p) + 3p(8 -r)

12r + 16pr + 24p + -3pr

12r + (16pr - 3pr) + 24p

12r + 13pr + 24p

3. (3 + 2h)(5 + 3h)

3(5 + 3h) + 2h(5+3h)

15 + 9h + 10h + 6h^2

6h^2 + 19h + 15

4. (3 + 4y)(5y - 1)

3(5y - 1) + 4y(5y - 1)

15y - 3 + 20y^2 - 4y

20y^2 + 11y - 3

5. (2n - 3p)(3p - 2m)

2n(3p - 2m) + -3p(3p - 2m)

6np - 4mn + -9p^2 + 6mp

-9p^2 - 4mn + 6mp + 6np

Hope this helps!