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 :

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

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 :

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

This option is false.

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

Answer 2

Answer

−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.

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.