Question

Упростите выражение:
1) (х + 3)(х – 7) - 4x(5 – 2х);
2) (x + 2)(у – 6) + (у + 3)(у – 4);
3) (х – 3)(3х + 1) - (2x + 3)(4х – 1);
4) (2а - 3b)(7а + 4b) - (3,5а + b)(4а - 6b);
5) (m3 – 3n)(m2 + 2n) — 4*(m2 + 7n).​

Answer 1

$\left(x+3\right)\left(x-7\right)-4x\left(5-2x\right)=\\=x^2-4x-21-4x\left(5-2x\right)=\\=x^2-4x-21-20x+8x^2=\\=9x^2-24x-21$

$\left(x+2\right)\left(y-6\right)+\left(y+3\right)\left(y-4\right)=\\=xy-6x+2y-12+y^2-y-12=\\=y^2+xy+y-6x-24$

$\left(x-3\right)\left(3x+1\right)-\left(2x+3\right)\left(4x-1\right)=\\=3x^2-8x-3-8x^2-10x+3=\\=-5x^2-18x$

$\left(2a-3b\right)\left(7a+4b\right)-\left(3.5a+b\right)\left(4a-6b\right)=\\=14a^2-13ab-12b^2-14a^2+17ab+6b^2=\\=4ab-6b^2$

$\left(m^3-3n\right)\left(m^2+2n\right)-4\left(m^2\:+7n\right)=\\=m^5+2m^3n-3m^2n-6n^2-4\left(m^2+7n\right)=\\=m^5+2m^3n-3m^2n-6n^2-4m^2-28n$