Question

If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y? Show all the steps.

A) (a + 2b)²

B) (2a + 2b)²

C) (4a + 4b)²

D) (4a + 8b)²

Answer 1

Answer:

The answer to your question is:       (2a + 2b)²

Step-by-step explanation:

a² + b² = z

ab = y

Which is equivalent to 4z + 8y ?

Substitution

                                     4(a² + b²) + 8(ab)

Simplify                        4a² + 4b² + 8ab

Order                            4a² + 8ab + 4b²       It's a perfect square trynomial

Factorize                     (2a + 2b)²

Answer 2

The expression 4z + 8y is equivalent to the expression (2a + 2b)². Then the correct option is B.

What is an equivalent expression?

The equivalent is the expressions that are in different forms but are equal to the same value.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

If a² + b² = z and ab = y.

The equivalent to 4z + 8y will be

We know that the formula

(a + b)² = a² + b² + 2ab

Then substitute the value of a² + b² and 2ab, then the equation will be

(a + b)² = z + 2y

Multiply the equation by 4, then the equation will be

4(a + b)² = 4(z + 2y)

Simplify the equation, then the equation will be

(2a + 2b)² = 4z + 8y

The expression 4z + 8y is equivalent to the expression (2a + 2b)².

Then the correct option is B.

More about the equivalent link is given below.

https://brainly.com/question/889935

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