(a+b)^{2} -4c^{2} (a+b)+4c^{4}

4c4−4ac2−4bc2+a2+2ab+b2

Step-by-step explanation:

4c4+(a+b)2−4c2(a+b),

(a+b)2 and −4c2(a+b).

4c4−4c2(a+b)+(a+b)2

Factor −4 out of −4c2(a+b).

4c4−4(c2(a+b))+(a+b)2

Rewrite −4 as −2 plus −2

4c4+(−2−2)(c2(a+b))+(a+b)2

Apply the distributive property.

4c4−2(c2(a+b))−2(c2(a+b))+(a+b)2,

4c4−2c2(a+b)−2(c2(a+b))+(a+b)2,

4c4−2c2(a+b)−2c2(a+b)+(a+b)2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4c4−2c2(a+b))−2c2(a+b)+(a+b)2

Factor out the greatest common factor (GCF) from each group.

2c2(2c2−1(a+b))−(a+b)(2c2−(a+b))

Factor the polynomial by factoring out the greatest common factor,

2c2−1(a+b).

(2c2−1(a+b))(2c2−(a+b))

Apply the distributive property.

(2c2−1a−1b)(2c2−(a+b))

Rewrite −1a as −a.

(2c2−a−1b)(2c2−(a+b))

Rewrite −1b as −b.

(2c2−a−b)(2c2−(a+b))

Apply the distributive property.

(2c2−a−b)(2c2−a−b)