simplify (2\5x²+3y²)(5x²-4\7y²)
Answers
Answer:
GIVEN :
Simplify : \frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
)
TO FIND :
The simplified terms of the given expression \frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
)
SOLUTION :
Given expression is \frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
)
Now solving the given expression as below :
\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
)
=\frac{2}{7}(7(2x^2-3y^2))(-5x^2-3y^2)=
7
2
(7(2x
2
−3y
2
))(−5x
2
−3y
2
)
=2(2x^2-3y^2)(-5x^2-3y^2)=2(2x
2
−3y
2
)(−5x
2
−3y
2
)
=2(2x^2)-2(3y^2)(-5x^2-3y^2)=2(2x
2
)−2(3y
2
)(−5x
2
−3y
2
)
By using the Distributive property :
a(x-y)=ax-ay
=(4x^2-6y^2)(-5x^2-3y^2)=(4x
2
−6y
2
)(−5x
2
−3y
2
)
=4x^2(-5x^2-3y^2)-6y^2(-5x^2-3y^2)=4x
2
(−5x
2
−3y
2
)−6y
2
(−5x
2
−3y
2
)
By using the Distributive property :
(a+b)(x+y)=(a+b)x+(a+b)y
=4x^2(-5x^2)+4x^2(-3y^2)-6y^2(-5x^2)-6y^2(-3y^2)=4x
2
(−5x
2
)+4x
2
(−3y
2
)−6y
2
(−5x
2
)−6y
2
(−3y
2
)
By using the Distributive properties :
i) a(x+y)=ax+ay
ii) a(x-y)=ax-ay
By using the exponent property :
a^m.a^n=a^{m+n}a
m
.a
n
=a
m+n
=-20x^4-12x^2y^2+30x^2y^2+18y^4=−20x
4
−12x
2
y
2
+30x
2
y
2
+18y
4
=-20x^4+18x^2y^2+18y^4=−20x
4
+18x
2
y
2
+18y
4
\frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)=-20x^4+18x^2y^2+18y^4
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
)=−20x
4
+18x
2
y
2
+18y
4
∴ the simplified terms for the given expression \frac{2}{7}(14x^2-21y^2)(-5x^2-3y^2)
7
2
(14x
2
−21y
2
)(−5x
2
−3y
2
) is -20x^4+18x^2y^2+18y^4−20x
4
+18x
2
y
2
+18y
4