Question

Perform the indicated operations and simplify completely:
(x-7) (x+1) - (x+8) (x-7)

Answer 1

Explanation:

To simplify the expression, we can use the distributive property to expand each of the terms:

(x-7) (x+1) - (x+8) (x-7)

= x(x+1) - 7(x+1) - x(x-7) + 8(x-7)

Then, we can simplify the expression by combining like terms:

= x^2 + x - 7x - 7 + x^2 - 7x + 8x - 56

= 2x^2 - 14x + 49

So the simplified expression is 2x^2 - 14x + 49.

I hope this helps! Let me know if you have any questions.

Answer 2

–7x + 49

Explanation:

( x – 7 )( x + 1 ) — ( x + 8 )( x – 7 )

by expanding each bracket

x(x+1) –7(x+1) — (x(x–7) +8(x–7))

= x² + x –7x –7 —( x² –7x + 8x – 56)

by using (–) to simplify the other brackets

= x² –6x – 7 – x² + 7x – 8x + 56

Then collecting like terms

= x² – x² –6x + 7x – 8x – 7 + 56

= x – 8x + 49

= –7x + 49

i hope this helps