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Popular >

expand (t^2+2t+1)^2

Solution

expand

(t^{2} + 2 t + 1)^{2}

Solution

t^{4} + 4 t^{3} + 6 t^{2} + 4 t + 1

Solution steps

(t^{2} + 2 t + 1)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(t^{2} + 2 t + 1)^{2} = (t^{2} + 2 t + 1) (t^{2} + 2 t + 1)

= (t^{2} + 2 t + 1) (t^{2} + 2 t + 1)

Distribute parentheses

= t^{2} t^{2} + t^{2} \cdot 2 t + t^{2} \cdot 1 + 2 t t^{2} + 2 t \cdot 2 t + 2 t \cdot 1 + 1 \cdot t^{2} + 1 \cdot 2 t + 1 \cdot 1

Simplify

t^{2} t^{2} + t^{2} \cdot 2 t + t^{2} \cdot 1 + 2 t t^{2} + 2 t \cdot 2 t + 2 t \cdot 1 + 1 \cdot t^{2} + 1 \cdot 2 t + 1 \cdot 1 : t^{4} + 4 t^{3} + 6 t^{2} + 4 t + 1

= t^{4} + 4 t^{3} + 6 t^{2} + 4 t + 1

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Frequently Asked Questions (FAQ)

What is expand (t^2+2t+1)^2 ?
The solution to expand (t^2+2t+1)^2 is t^4+4t^3+6t^2+4t+1