Question

Simplify and verify the results for
$( {7x}^{3} + {8x}^{2} - 3)( {x}^{2} - 5) \: \: \: x = 5$
I need step by step explanation​

Answer 1

Answer:

21440

Step-by-step explanation:

Simplify:

• (7x³ + 8x² - 3)(x² - 5)

Start by multiplying 7x³ by x² and -5.

• 7x⁵ - 35x³ + (8x² - 3)(x² - 5)    

Multiply 8x² by x² and -5.

• 7x⁵ - 35x³ + 8x⁴ - 40x² + (-3)(x² - 5)

Multiply -3 by x² and -5.

• 7x⁵ - 35x³ + 8x⁴ - 40x² -3x² + 15

Combine like terms together.

• 7x⁵ - 35x³ + 8x⁴ - 43x² + 15

Rearrange the terms in descending power order.

• 7x⁵ + 8x⁴ - 35x³ - 43x² + 15  

Verify (I):

Substitute x = 5 into the above polynomial.

• 7(5)⁵ + 8(5)⁴ - 35(5)³ - 43(5)² + 15

Evaluate the exponents first.

• 7(3125) + 8(625) - 35(125) - 43(25) + 15

Multiply the terms together.

• 21875 + 5000 - 4375 - 1075 + 15

Combine the terms together.

• 21440

This is the answer when substituting x = 5 into the simplified expression.

Verify (II):

Substitute x = 5 into the expression.

• [7(5)³ + 8(5)² - 3][(5)² - 5]

Evaluate the exponents first.

• [7(125) + 8(25) - 3][(25) - 5]

Multiply the terms in the first bracket next.

• [875 + 200 - 3][25 - 5]

Evaluate the expressions inside the brackets.

• [1072][20]

Multiply these two terms together.

• 21440

This is the answer when substituting x = 5 into the original (unsimplified) expression.