Question

Type the correct answer in each box. Use numerals instead of words.

Multiply the expressions.
b=
.C=
3x²+2z-21
-22²-2x+12
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
az +b
cz + d
and d =
.
2z²+25z +63
6z²+72-49

Answer 1

To multiply the expressions, substitute the expressions into b, c, and d and simplify. Then, when a = 1, substitute a = 1 into the expressions to find the values of b, c, and d.

Step-by-step explanation:

Problem

Multiply the expressions:

b = (3x²+2z-21) * (-22²-2x+12)

c = (3x²+2z-21) * (2z²+25z +63)

d = (3x²+2z-21) * (6z²+72-49)

Solution

Step 1: Simplify the expressions in parentheses.

b = (3x²+2z-21) * (484-2x+12)

c = (3x²+2z-21) * (2z²+25z +63)

d = (3x²+2z-21) * (6z²+72-49)

Step 2: Multiply the simplified expressions.

b = 1452x² - 176x - 992z² + 48z + 9936

c = 6z⁴ + 75z³ + 243z² - 441z - 3726x² + 702x + 9111

d = 18z⁴ + 216z³ - 294z² - 462z - 7944x² + 1494x + 19404

If a = 1

To find the values of b, c, and d when a = 1, substitute a = 1 into the expressions.

b = 1452 - 176 - 992z² + 48z + 9936

c = 6z⁴ + 75z³ + 243z² - 441z - 3726 + 702 + 9111

d = 18z⁴ + 216z³ - 294z² - 462z - 7944 + 1494 + 19404

Simplified Expressions

b = -176 - 992z² + 48z + 11088

c = 6z⁴ + 75z³ + 243z² - 441z - 3021 + 702 + 9111

d = 18z⁴ + 216z³ - 294z² - 462z + 4002 + 1494 + 19404

Result

b = -992z² + 48z - 176 + 11088

c = 6z⁴ + 75z³ + 243z² - 441z + 3432

d = 18z⁴ + 216z³ - 294z² - 462z + 25308