Question

Ab³ (5a²-4ab+b²) multiply

Answer 1

Answer: The correct answer is 5a^3b^3 − 4a^2b^4 + ab^5

Explanation:

ab^3 (5a^2 − 4ab + b^2)

Multiply together:

(ab^3)*(5a^2 + −4ab + b^2)

(ab^3)*(5a^2) + (ab^3)*(−4ab) + (ab^3)*(b^2)

= 5a^3b^3 − 4a^2b^4 + ab^5

Answer 2

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

Explanation:

Given expression:

`ab^3(5a^2-4ab+b^2)`

Apply the distributive property a(b - c + d) = ab - ac + ad :

`\implies ab^3 \cdot5 a^2-ab^3 \cdot 4ab+ab^3 \cdot b^2`

Collect like terms:

`\implies 5aa^2b^3-4aabb^3+ab^2b^3`

Apply the exponent rule a = a¹ :

`\implies 5a^1a^2b^3-4a^1a^1b^1b^3+a^1b^2b^3`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies 5a^((1+2))b^3-4a^((1+1))b^((1+3))+a^1b^((2+3))`

Simplify:

`\implies 5a^3b^3-4a^2b^4+ab^5`