Question

6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab) iii) (b2 – 49) (b + 7) + 343 okay, I know I posted this question before but, if you're giving your answers, please explain how you got it,

Answer 1

Answer:

Step-by-step explanation:

6. I will multiply then  I respect the sign rules

- * -  =   +

- * + =  -

I will atach the file immediately.

I  multiplied the paranthesis and  then I added the results

Answer 2

Answer:

i)6a^2-2ab-6b^2

ii)ab^2-1a^2b

iii)b^3-42b

Step-by-step explanation:

Use distributive property

Collect like terms

(a+b)(5a-3b)+(a-3b)(a-b)

(a+b)(5a-3b)---- Distributive property

5a^2-3ab+5ab-3b^2

5a^2+5ab-3ab-3b^2

5a^2+2ab-3b^2

(a-3b)(a-b)

a^2-ab-3ab-3b^2

a^2-4ab-3b^2

So,

5a^2+2ab-3b^2+a^2-4ab-3b^2---Collect like terms

5a^2+a^2+2ab-4ab-3b^2-3b^2

6a^2-2ab-6b^2

(a–b)(a^2+b^2 +ab)–(a + b)(a^2+b^2 –ab)

(a–b)(a^2+b^2 +ab)----Distributive property

a^3 since a^(1+2)=a^3

a^3+ab^2+a^2b-ba^2-b^3-ab^2

a^3+ab^2-ab^2+a^2b-ba^2-b^3

a^3+a^2b-a^2-b^3

a^3-b^3

(a+b)(a^2+b^2-ab)

a^3+ab^2-a^2b+ba^2+b^3-a^2b

a^3+ab^2+ba^2+b^3-a^2b-a^2b

a^3+ab^2+ba^2+b^3-2a^2b

So,

a^3-b^3-a^3+ab^2+ba^2+b^3-2a^2b--Collect like terms

a^3-a^3-b^3+b^3+ab^2-2a^2b+a^2b

ab^2-1a^2b

(b^2–49)(b + 7)+343---Distributive property

b^3+7b-49b-343+343---Collect like terms

b^3-49b+7b

b^3-42b

Hope this helps ;) ❤❤❤