Question

4. Find the product of(1/2x³ ) × (-10x) × (1/5x²)
and verify the result for x = 1.​

Answer 1

Explanation:

Find the product of(1/2x³ ) × (-10x) × (1/5x²)

and verify the result for x = 1.

Answer 2

ANSWER:

The product of the given terms = - x⁶.

GIVEN:

(1/2 x³) × (-10 x) × (1/5 x²)

x = 1

TO FIND:

The product of the given terms.

\begin{gathered} \\ \\ \end{gathered}

TO VERIFY:

The result for x = 1.

\begin{gathered} \\ \\ \end{gathered}

EXPLANATION:

$\begin{gathered} \sf \dashrightarrow\dfrac{1}{2} x^3 \times (-10 x) \times \dfrac{1}{5} x^2 \\ \\ \end{gathered} </p><p>⇢$

1/2 x^ 3 ×(−10x)× 1/5 x^ 2

$\begin{gathered}\sf \dashrightarrow\dfrac{1}{2}( - 10) (x^3) (x)\times \dfrac{1}{5} x^2 \\ \\ \end{gathered} </p><p>⇢$

1/2 (−10)(x^3 )(x)× 1/5 x^2

$\begin{gathered}\sf \dashrightarrow( - 5) x^4 \times \dfrac{1}{5} x^2 \\ \\ \end{gathered} </p><p>⇢(−5)x$

$\begin{gathered}\sf \dashrightarrow\dfrac{1}{5}( - 5) (x^4) (x^2) \\ \\ \end{gathered} </p><p>⇢$

1 (−5)(x 4 )(x 2 )

$\begin{gathered}\sf \dashrightarrow - x^6\\ \\ \end{gathered} </p><p>⇢−x$

6

$\begin{gathered} \boxed{ \bold{\red{\dfrac{1}{2} x^3 \times (-10 x) \times \dfrac{1}{5} x^2 = - {x}^{6} }}} \\ \\ \end{gathered}$

1/3 x 3 ×(−10x)× 1/5 x 2 =−x 6

VERIFICATION:

$\begin{gathered} \sf \leadsto \dfrac{1}{2} x^3 \times (-10 x) \times \dfrac{1}{5} x^2 = - {x}^{6} \\ \\ \end{gathered} </p><p>⇝$

$\begin{gathered}\textbf{ \pink{Substitute x = 1}} \\ \\ \end{gathered} </p><p> Substitute x = 1</p><p>$

$\begin{gathered} \sf \leadsto \dfrac{1}{2}(1)^3 \times (-10 (1)) \times \dfrac{1}{5} (1)^2 = - {1}^{6} \\ \\ \end{gathered} </p><p>⇝$

2

1

(1)

3

×(−10(1))×

5

1

(1)

2

=−1

6

$\begin{gathered} \sf \leadsto \dfrac{1}{2}(1) \times (-10) \times \dfrac{1}{5} (1) = - 1 \\ \\ \end{gathered} </p><p>⇝$

2

1

(1)×(−10)× 1/5 (1)=−1

$\begin{gathered} \sf \leadsto \dfrac{1}{2} \times (-10) \times \dfrac{1}{5} = - 1 \\ \\ \end{gathered} </p><p>⇝$

2

1

×(−10)× 1/5 =−1

$\begin{gathered} \sf \leadsto \dfrac{1}{10} \times (-10) = - 1 \\ \\ \end{gathered} </p><p>⇝$

1/10 ×(−10)=−1

$\begin{gathered} \sf \leadsto - 1 = - 1 \\ \\ \end{gathered} </p><p>⇝−1=−1</p><p>$

HENCE VERIFIED.