Math Problem Statement

(3 + x) · (y + 4) + (4x)^2 · 2

Solution

The expression in the image is:

(3+x)(y+4)+(4x)22(3 + x) \cdot (y + 4) + (4x)^2 \cdot 2

Let's simplify this step-by-step:


Step 1: Expand the first term (3+x)(y+4)(3 + x) \cdot (y + 4)

Using the distributive property: (3+x)(y+4)=3y+12+xy+4x(3 + x) \cdot (y + 4) = 3y + 12 + xy + 4x So, the expanded form is: 3y+xy+12+4x3y + xy + 12 + 4x


Step 2: Simplify (4x)22(4x)^2 \cdot 2

First, calculate (4x)2(4x)^2: (4x)2=16x2(4x)^2 = 16x^2 Now multiply it by 2: 16x22=32x216x^2 \cdot 2 = 32x^2


Step 3: Combine all terms

Now add the results of Step 1 and Step 2: 3y+xy+12+4x+32x23y + xy + 12 + 4x + 32x^2

This is the fully simplified expression: 32x2+xy+4x+3y+1232x^2 + xy + 4x + 3y + 12


Final Answer:

32x2+xy+4x+3y+12\boxed{32x^2 + xy + 4x + 3y + 12}


Would you like me to expand on this further or solve for specific values of xx and yy?

Related Questions:

  1. What is the value of this expression for specific xx and yy?
  2. How do you factorize this expression?
  3. What is the degree of this polynomial with respect to xx?
  4. What happens when x=0x = 0 or y=0y = 0?
  5. How can we graph this expression for xx and yy?

Tip:

Always expand brackets carefully step-by-step to avoid errors, especially when there are multiple terms!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Distributive Property

Formulas

Distributive property: a(b + c) = ab + ac
Power rule: (a^m)^n = a^(m·n)

Theorems

Basic polynomial expansion

Suitable Grade Level

Grades 8-10