代数表达式

练习9.4

问题1:二项式相乘。

(我)' (2x + 5) '和' (4x - 3) '

答:' (2x + 5)(4x - 3) '
' = 2x × 4x - 2x × 3 + 5 × 4x - 5 × 3 '
' = 8x^2 - 6x + 20x -15 '
' = 8x²+ 14x -15 '

(2)' (y - 8) '和' (3y - 4) '

答:(y - 8)(3y - 4) '
' = y × 3y - 4y - 8 × 3y + 32 '
' = 3y^2 - 4y - 24y + 32 '
' = 3y^2 - 28y + 32 '

(3)(2.5l - 0.5m)和(2.5l + 0.5m)

答:(2.5升+ 0.5米)
使用' (a+b)(a-b) = a^2 -b ^2 '
得到= 6.25 l^2 - 0.25 m^2

(iv)' (a + 3b) '和' (x + 5) '

答:' = ax + 5a + 3bx + 15b '

(v) ' (2pq + 3q^2) '和' (3pq - 2q^2) '

答:' = 2pq × 3pq - 2pq × 2q^2 + 3q^2 × 3pq - 3q^2 × 2q^2 '
' = 6p^2q^2 - 4pq^3 + 9pq^3 - 6q^4 '
' = 6p^2q^2 - 5pq^3 - 6p^4 '

(vi)”(3/4a ^ 2 + 3 b ^ 2) xx4 (^ 2-2/3b ^ 2)”

答:' = 3/4a ^ 2 \ xx4a ^ 2-3/4a ^ 2 \ xx8/3b ^ 2 + 12 a ^ 2 b ^ 2-8b ^ 2》

3 ' = ^ 4-2a ^ 2 ^ 2 + 12 a ^ 2 ^ 2-8b ^ 4 '

3 ' = ^ 4-8b ^ 2 + 10 ^ 2 b ^ 2》

问题2:求乘积。

(我)' (5 - 2x) (3 + x) '

答:' = 15 + 5x - 6x - 2x^2 '
' = 15 - x - x^2 '

(2)' (x + 7y) (7x - y) '

答:' = 7x²- xy + 49xy - 7y²'
' = 7x²- 7y²+ 48xy '

3)' (a²+ b) (a + b²)'

答:' a^2 xx\ a + a^2 xx\b + a\ xx\b + b^3 '
' = a^3 + a^2b + ab + b^3 '
' = a^3 + b^3 + a^2b + ab '

(iv)' (p²- q²)(2p + q) '

答:' = 2p^3 + p^2q - 2pq^2 - q^3 '
' = 2p^3 - q^3 + p^2q - 2pq^2 '

问题3:简化。

(我)' (x^2 - 5) (x + 5) + 25 '

答:' = x^3 + 5x^2 - 5x - 25 + 25 '
= x^3 + 5x^2 -5x '

(2)(a^2+ 5) (b^3+ 3) + 5 '

答:' a^2b^3 + 3a^2 + 5b^3 + 15 + 5 '
' = a^2b^3 + 5b^3 + 3a^2 + 20 '

(iv)' (a + b) (c - d)+ (a - b) (c + d) + 2 (ac + bd) '

答:' = (ac - ad + bc - bd) + (ac +广告- bc - bd) ' ' + (2 ac + 2 bd) '
' = ac - AD + BC - bd + ac + AD - BC ' ' - bd + 2ac + 2bd= 4ac '

(v)' (x + y)(2x + y) + (x + 2y)(x - y) '

答:' =2x²+ xy + 2xy + y²+ x²- xy + 2xy - 2y²'
' = 3x²+ 4xy - y²'

(vi)' (x + y)(x²- xy + y²)'

答:= x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3 '
' = x³+ y³'

(七)(1.5x + 4y + 3) - 4.5x + 12y '

答:' = 2.25x^2 + 6xy + 4.5x - 6xy - 16y^2 ' - 12y - 4.5x + 12y '
' = 2.25x²- 16y²'

(八)' (a + b + c)(a + b - c) '

答:' = a²+ ab - ac + ab + b²- BC + ac + BC - c²'
' = a²+ b²- c²+ 2ab '