Question

Which equations are correct? Select each correct answer. −5a4(2a2+4)=−10a6−20a4 −4x2(2x2+5)=−8x4−20x2 −6y4(4y2+2)=−24y8−12y4 −4b3(5b2+3)=−20b6−12b3

Answer 1

1. Consider the expression
`-5a^4(2a^2+4)=-10a^6-20a^4.`

Start with left side and use dustributive property :

`-5a^4(2a^2+4)=-5a^4\cdot 2a^2-5a^4\cdot 4=-10a^6-20a^4.`

This option is true.

2. Consider the expression
`-4x^2(2x^2+5)=-8x^4-20x^2.`

Start with left side and use dustributive property :

`-4x^2(2x^2+5)=-4x^2\cdot 2x^2-4x^2\cdot 5=-8x^4-20x^2.`

This option is true.

3. Consider the expression
`-6y^4(4y^2+2)=-24y^8-12y^4.`

Start with left side and use dustributive property :

`-6y^4(4y^2+2)=-6y^4\cdot 4y^2-6y^4\cdot 2=-24y^6-12y^4\\eq -24y^8-12y^4.`

This option is false.

4. Consider the expression
`-4b^3(5b^2+3)=-20b^6-12b^3.`

Start with left side and use dustributive property :

`-4b^3(5b^2+3)=-4b^3\cdot 5b^2-4b^3\cdot 3=-20b^5-12b^3\\eq -20b^6-12b^3.`

This option is false.

Answer: A, B - true, C, D - false.

Answer 2

−5a⁴(2a²+4)=−10a⁶−20a⁴ is correct.

−4x²(2x²+5)=−8x⁴−20x² is correct.

−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.

−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.

Step-by-step explanation

Equation 1

−5a⁴(2a²+4)=−10a⁶−20a² ⇒ −5a⁴(2a²+4) = ( −5a⁴×2a²)+ ( −5a⁴×4)

= -10a⁶ - 20a⁴

−5a⁴(2a²+4)=−10a⁶−20a² is correct

Equation 2

−4x²(2x²+5)=−8x⁴−20x² ⇒ −4x²(2x²+5) = (-4x²×2x²) + (-4x²×5)

= -8x⁴ - 20x²

−4x²(2x²+5)=−8x⁴−20x² is correct.

Equation 3

−6y⁴(4y²+2)=−24y⁸−12y⁴ ⇒ −6y⁴(4y²+2) = (−6y⁴×4y²) + (-6y⁴×2)

= -24y⁶ - 12y⁴

−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.

Equation 4

−4b³(5b²+3)=−20b⁶−12b³ ⇒ −4b³(5b²+3) = (−4b³×5b²) + (-4b³×3)

= -20b⁵ - 12b³

−4b³(5b²+3)=−20b⁶−12b³ is NOT correct.