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## A Plus B Whole Four (a+b)^4

Are you looking for a plus b whole four? You can check the formulas of a plus b whole four in three ways. We are going to share the (a+b)^4 algebra formulas for you as well as how to create (A+B)^4 and proof.

we can write $$(a+b)^4 = (a+b)^2 \times (a+b)^2$$

[Note: We know a plus b whole square formula: $$(a+b)^2 = a^2 + b^2 +2ab$$]

$$(a+b)^4 = (a^2 + b^2 +2ab) \times (a^2 + b^2 +2ab)$$

Brack braket into multiplciation form

$$(a+b)^4 = (a^2 + b^2 +2ab) \times a^2 \\ + (a^2 + b^2 +2ab) \times b^2 \\ + (a^2 + b^2 +2ab) \times 2ab$$

start multiplication

$$(a+b)^4 = (a^4 + b^2 a^2 +2a^3b) \\ + (a^2 b^2+ b^4 +2ab^3) \\ + (2a^3b + 2ab^3 +4a^2b^2)$$

simplify Calculation with arrage power and same value

$$(a+b)^4 = a^4 + b^4 + 6a^2b^2 + 4a^3b +4b^3a$$

we can also write like this $$(a+b)^4 = a^4 + b^4 + 6a^2b^2 + 4ab (a^2 + b^2)$$

### (A+B)^4 Verifications

Need to verify $$(a+b)^4$$ formula is right or wrong. put the value of a =1 and b=2

put the value of a and b in the LHS

$$=> (a+b)^4 = (1+2)^4$$

$$=> (a+b)^4 = (3)^4$$

$$=> (a+b)^4 = 81$$

put the value of a and b in the RHS

$$a^4 + b^4 + 6a^2b^2 + 4ab (a^2 + b^2)$$

$$1^4 + 2^4 + 6 \times 1^2 \times 2^2 + 4\times 1\times 2 (1^2 + 2^2)$$

Simplify calculation: $$1 + 16 + 6 \times 1 \times 4 + 4\times 1\times 2 (1 + 4)$$

$$1 + 16 + 24 + 8 (5)$$

$$1 + 40 + 40 = 81$$

Therefore $$LHS =RHS$$ [Note: LHS =Left hand Side, RHS =Right hand side]

#### Summary (A+B)^4

If you have any issues in the (A+B)^4 formulas, please let me know through social media and mail. A Plus B Whole Four is the most important algebra maths formulas for class 6 to 12.

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