§ 44: 44.31

44.31 Спростіть вираз:

1) a12+ 2a14 b14+b12a76 • b56-a56 • b76 • a-a13 b23 a14 b14 + b12 = (a14 + b14)21• a13(a23 - b23) a56b56 a26 - b26 • b14(a14 + b14) = a13 • a14 + b14 • (a13 - b13)(a13 + b13)a56b56 • b14(a13 - b13) = (a14 + b14)(a13 + b13)a12 • b1312.

2) a32+b32(a2 -ab)23 : a-23 • (a-b)13a32-b32 = (a32 + b32)(a32 - b32)a-23 • (aa- b)23(a- b)13 = (a3 - b3)a23a23•(a- b)23 •(a- b)13 = (a- b)(a2 +ab+ b2)a- b = a² + ab + b².

3) (1 – a136)(1 + a136 + a118) + 4- a162-a112 = (1 – a112) + (2- a112)(2+ a112)2- a112 = (1 – a112 + 2 + a112 = 3.

4) m43-27m13 nm23+33mn+9n23 : (1 – 33nm) – 3m2 = m13 (m-27n)m23+3mmn+9n23 • 11-33nm – 3m2 = m13 • (m13 – 3n13) • m13m13-3n13 – 3m2 = m23 – m23 = 0.