Simplify: $(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$

m^{4} + m^{2} n^{4} + 4 m^{3} n^{2}

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m^{4} + m^{4} n^{2} + 4 m^{3} n^{2}

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m^{2} + m^{4} n^{2}

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m^{4} + m^{2} n^{4}

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Solution

The correct option is D $m^{4} + m^{2} n^{4}$
$(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2} = (m^{2})^{2} + (n^{2} m)^{2} - 2 \times m^{2} \times n^{2} m + 2 m^{3} n^{2} = m^{4} + n^{4} m^{2} - 2 m^{3} n^{2} + 2 m^{3} n^{2} = m^{4} + n^{4} m^{2} = m^{4} + m^{2} n^{4}$

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Similar questions

(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}

(m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}

Simplify: (m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}

Simplify:

$(i) (x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})$ $(i i) (2 x - 1) (2 x + 1) (4 x^{2} + 1) (16 x^{4} + 1)$

$(i i i) (7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ $(i v) (2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$

$(v) (m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$

Simplify.

(i) (a² − b²)²(ii) (2x +5)² − (2x − 5)²

(iii) (7m − 8n)² + (7m + 8n)² (iv) (4m + 5n)² + (5m + 4n)²

(v) (2.5p − 1.5q)² − (1.5p − 2.5q)²

(vi) (ab + bc)² − 2ab²c (vii) (m² − n²m)² + 2m³n²

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